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LIBRARY 

OF  THK 

UNIVERSITY  OF  CALIFORNIA. 


OF" 

V 
Accession        85969  Class 


HEATH'S 
PRIMARY    ARITHMETIC 


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3 

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HEATH'S 


PRIMARY  ARITHMETIC 


BY 

CHARLES   E.    WHITE 

\\ 
AND 

BRUCE   M.   WATSON 

SYRACUSE,  N.Y. 


BOSTON,   U.S.A. 

D.    C.    HEATH   &   CO.,    PUBLISHERS 
1901 


COPYRIGHT,   1901, 
BY  D.  C.  HEATH  &  Co. 


PREFACE 


IN  education,  as  in  other  affairs  of  life,  there  is  a  tendency,  on  the  part 
of  many,  to  pursue  good  ideas  to  unreasonable  extremes,  and  ofttimes  to  the 
exclusion  of  other  ideas  quite  as  good. 

This  book  has  been  prepared  with  the  design  of  bringing  together  the 
manifest  advantages  of  the  topically  arranged  text-book  and  the  equally 
manifest  advantages  of  the  so-called  "  spiral "  plan. 

Each  subject  is  treated  by  itself  as  exhaustively  as  the  scope  and  purpose 
of  tl$  book  will  warrant.  At  the  same  time  each  new  subject  introduced  is 
considered  in  all  its  relations  with  and  bearing  upon  preceding  subjects. 

By  the  great  abundance  and  variety  of  the  drill  work  and  problems 
throughout  the  book,  all  subjects  are  kept  in  constant  review,  every  principle 
is  applied  in  as  many  ways  as  possible,  and  the  unity  of  the  'book  is 
preserved. 

The  order  of  subjects  is  determined  by  the  law  of  dependence,  the  degree 
of  simplicity  of  the  matter  to  be  taught,  and  the  relative  importance  of  the 
respective  subjects  in  the  business  of  life. 

The  development  of  the  various  principles  and  processes  has  been  written 
with  great  care  and  considerably  in  detail,  with  a  view  both  to  furnish  the 
teacher  a  definite  plan  for  presenting  the  work  and  to  help  the  student  in 
his  efforts  toward  independent  achievement. 

Both  the  method  and  the  matter  of  the  book  have  been  tested  by  actual 
use  in  the  schoolroom  ;  they  are  not  in  any  sense  an  experiment. 

Part  I  is  a  strictly  primary  arithmetic.  The  first  few  lessons  are  extremely 
simple,  yet  they  furnish  an  illustration  of  the  logical  steps  in  the  develop- 
ment of  ideas  of  number.  If  any  child  begins  the  use  of  the  book  with 
elementary  notions  of  number  already  developed  in  his  mind  to  a  certain 
point,  the  judicious  teacher  will  be  wise  enough  to  begin  where  the  child's 
previously  acquired  knowledge  stops. 

The  development  work  preceding  each  table  is  designed  to  give  the  child 
a  concrete  understanding  of  the  processes  by  which  the  table  is  made  instead 
of  forcing  him  to  memorize  abstract  results  obtained  by  making  arbitrary 
combinations.  But  after  a  table  has  been  thoroughly  developed,  the  pupil 

85969 


VI  PREFACE 

should  be  drilled  in  all  its  combinations  until  he  can  give  results  instantly 
without  reference  to  the  mental  processes  by  which  they  may  be  obtained. 
To  this  end  the  drill  charts  should  be  used  daily  until  all  results  can  be  given 
correctly  without  an  instant's  hesitation. 

The  problems  following  the  tables  were  selected  from  lessons  given  by 
scores  of  successful  primary  teachers,  and  it  is  believed  that  they  are  far 
richer  in  variety  of  work  and  forms  of  statement  than  any  list  prepared  by 
a  single  individual. 

Part  II  is  an  introduction  to  written  arithmetic  proper.  The  color  work, 
both  here  and  in  Part  I,  is  introduced  not  merely  to  embellish  the  pages, 
but  rather  to  furnish  the  best  means  of  illustration  and  practice  in  certain 
arithmetical  operations. 

Much  of  the  mental  work  in  Part  II  may  be  used  as  supplementary  to  the 
questions  in  Part  I. 

Definitions  are  given  only  when  and  where  they  are  needed. 

In  the  treatment  of  fractions  the  fact  that  a  fraction  is  an  expression  of 
division  is  kept  prominent. 

Throughout  the  book  the  authors  have  endeavored  to  insert  whatever  may 
help  the  pupil  to  an  understanding  of  principles  ;  to  omit  whatever  is  super- 
fluous or  may  tend  to  confusion. 

B.  M.  W. 

SYRACUSE,  February  8,  1901. 


TABLE   OF  CONTENTS 

PART   I 

PAGE 

NOTATION  AND  NUMERATION 1 

ADDITION 7 

SUBTRACTION   ............  20 

MULTIPLICATION      ...........  31 

DIVISION 42 

PAET    II 

NOTATION  AND  NUMERATION  .........  75 

Arabic      . 77 

Roman 80 

Federal  Money .82 

ADDITION 83 

SUBTRACTION 94 

REVIEW  PROBLEMS           ..........  102 

MULTIPLICATION      ...........  104 

DIVISION 113 

REVIEW  EXERCISES 124 

REVIEW  PROBLEMS 125 

FACTORING 130 

CANCELLATION 132 

GREATEST  COMMON  DIVISOR  .........  134 

LEAST  COMMON  MULTIPLE       .........  135 

INDICATED  OPERATIONS  ..........  137 

FRACTIONS 140 

REDUCTION  OF  FRACTIONS       .         .         .         .  * 143 

ADDITION  OF  FRACTIONS          .         .         . 152 ' 

SUBTRACTION  OF  FRACTIONS 154 

SUBTRACTION  OF  MIXED  NUMBERS 155 

MULTIPLICATION  OF  FRACTIONS      .         .         .        .         .         .        .         .156 

DIVISION  OF  FRACTIONS  .         .         .         .         .         .         .         .         .         .  161 

COMPLEX  FRACTIONS       .         .         .         .         .         .         .         .         ...  166 

THE  THREE  QUESTIONS  OF  RELATION    .......  167 

ALIQUOT  PARTS       ...........  170 

REVIEW  OF  FRACTIONS 172 

DECIMAL  FRACTIONS 176 

To  read  Decimals      .        .        . 179 

To  write  Decimals    ..........  180 

REDUCTION  OF  DECIMALS        .........  182 

vii 


viii  TABLE   OF   CONTENTS 


PAGE 

ADDITION  OF  DECIMALS          .........  184 

SUBTRACTION  OF  DECIMALS 185 

MULTIPLICATION  OF  DECIMALS 186 

DIVISION  OF  DECIMALS 188 

REVIEW  OF  DECIMALS 191 

BILLS  AND  ACCOUNTS      ..........  192 

DENOMINATE  NUMBERS    ..........  194 

Linear  Measures 194 

Surface  Measures 196 

Cubic  Measures 199 

Liquid  Measures 200 

Dry  Measures 202 

Avoirdupois  Weight 203 

Troy  Weight 205 

Apothecaries'  Weight 205 

Federal  Money 206 

Time 207 

Miscellaneous  Tables 208 

REDUCTION  OF  DENOMINATE  NUMBERS  .......  209 

Descending 211 

Ascending 212 

REVIEW  OF  REDUCTION  .                                    215 

ADDITION  OF  COMPOUND  NUMBERS 216 

SUBTRACTION  OF  COMPOUND  NUMBERS  .         .         .         .         .         .         .  217 

DIFFERENCE  BETWEEN  DATES         .         .         .         .         .         .         .         .  218 

MULTIPLICATION  OF  COMPOUND  NUMBERS      .         .         .         .         ...  219 

DIVISION  OF  COMPOUND  NUMBERS 220 

SURFACE  MEASUREMENTS         .........  221 

Plastering  and  Painting .         .  223 

Carpeting  Rooms 224 

Papering  Walls         .         .         .         .         .         .         .         .         .         .227 

Board  Measure 227 

VOLUME  MEASUREMENTS          .         .         .         .         .         .         .         .         .  228 

Wood  Measure         .        .        . 231 

Capacity  of  Cisterns 232 

Capacity  of  Bins 232 

PERCENTAGE 233 

SIMPLE  INTEREST     ...........  238 

TOPICAL  REVIEW    . .         .         .  241 

Notation  and  Numeration 241 

Common  Fractions 241 

Decimal  Fractions    ..........  242 

Denominate  Numbers 244 

ANSWERS          ............  247 


PRIMARY  ARITHMETIC 


PART   FIRST 

To  THE  TEACHER. — For  early  work  with  numbers,  a  "  counting 
table"  is  almost  a  necessity,  whatever  text-book  may  be  used. 
It  should  be  about  two  feet  high,  thirty  inches  wide,  and  six 
feet  to  fourteen  feet  in  length,  according  to  the  size  of  the  class. 
It  should  be  surrounded  by  a  slightly  raised  casing  to  prevent  the 
counters  from  falling  off. 

Toothpicks  and  shoepegs  are  very  good  to  use  as  counters,  on 
account  of  their  cheapness  and  convenience  of  handling. 

1.   Counters  are  in  a  pile  in  front  of  the  pupils. 

Take  one  counter. 

Put  another  one  with  it.     How  many? 

Put  another  with  it.     How  many  ? 

So  on  until  ten  have  been  taken. 

Take  three  counters ;  seven  counters ;  five ;  nine ; 
six  ;  four  ;  ten  ;  eight. 

Count  the  girls  in  the  class. 

Count  the  boys  in  the  class. 

How  many  fingers  have  you  on  your  right  hand? 
On  your  left  hand  ? 

i 


PRIMARY    ARITHMETIC 


How  many  fingers  have  you  on  both  hands  ? 
How  many  fingers  and  thumbs  have  you  ? 
Count  ten  with  your  eyes  shut. 

Give  much  drill  on  these  numbers,  using  counters  and  other 
objects. 

2.   Make  the  figures   1  ,   2,   3,   4,   5,   lo,   ^    8,   C|. 


Teacher  place  figure  1  on  blackboard,  and  pupils  take  as  many 
counters.  Teacher  place  figure  2  on  the  blackboard  and  children 
take  as  many  counters.  So  on  with  all  the  figures,  one  at  a 
time,  the  pupils  each  time  taking  as  many  sticks  as  the  figure 
means. 

Teacher  count  out  three,  five,  nine,  seven,  eight  sticks,  etc., 
and  pupils  make  figures  to  represent  them. 

Make  the  figure  to  tell  how  many  years  old  you  are. 
Make  the  figure  to  tell  how  many  fingers  you  have. 
Make  the  figure  to  tell  how  many  hands  and  feet 
you  have. 

Make  the  figure  to  tell  the  hour  for  coming  to  school. 
Much  drill  should  be  given  in  this  kind  of  work. 

How  many  leaves  on  this 
cherry  branch  ? 

How  many  cherries  ? 

Make  the  figure  that  tells 
how  many  leaves. 

Make  the  figure  that  tells 
how  many  cherries. 

Make  a  stem  holding  5  cher- 
ries; 8  cherries;  10  cherries. 


PRIMARY   ARITHMETIC 


How  many  roses  in  the 
picture  ? 

How  many  rosebuds  ? 

What    figure    tells    how 
many  roses  ? 

What    figure    tells    how 
many  buds  ? 

Count  the  roses  and  buds 
together. 

How  many  parts  has  a  wood- 

bine  leaf? 

Make  the  figure. 

How    many    leaves    are    there 

on  a  cl°ver  stem  ? 
Make  the  figure. 
Make  two  woodbine  leaves. 
Count  the  parts  in  the  two  leaves. 

Count  the  red  stripes  in  the  flag. 

Count  the  white  stripes. 

Make  the  figure  that  tells  how 
many  red  stripes. 

Make    the    figure    that    tells 
how  many  white  stripes. 

Count  all  the  stripes. 

Count    the    stars    in   the    bot- 
tom row. 

How  many  colors  in  the  flag  ? 

How  many  stripes  below  the  blue  field  ? 

How  many  red  stripes  below  the  blue  field? 


PRIMARY   ARITHMETIC 


Count    the    daisies    in    the 
picture. 

How  many? 

What     figure     tells     how 
many  ? 

Count  the  tall  daisies. 
Make  the  figure  that  tells 
how  many  are  not  tall. 
How  many  apples  are  in  this  picture  ? 
Make  the  figure  that  tells  how  many  apples. 
Count     the     red 
apples. 

Count  the  other 
apples. 

Make  the  figure 
that  tells  how  many 
red  apples. 

How  many  pears  are  there  in  the  picture  ? 
Make  the  figure  that  tells  how  many. 


One,   1.         Two,   2.         Three,    3.         Four,   4. 
Five,   5.         Six,    6.         Seven,    7. 
Eight,    8.       Nine,    9.      Ten,    10. 


PRIMARY   ARITHMETIC  5 

3.  Take  ten  sticks.  m 
Tie  them  in  a  bunch,  thus,    it 

Count  out  ten  such  bunches  and  tie  them  up. 

Call  each  bunch  "a  ten." 

Put  one  bunch  on  the  table.       fj  n 

Put  one  stick  beside  it,  thus,     ml 

How  many  sticks  are  there  ?          |  | 

Put  another  stick  with  it,  thus,    if  If 

How  many  sticks  are  there  ?          I J2 
Take  another  ten    and    put   three  with    it,     iijjj 
thus,  if  UHII 

How  many  are  there  ?  I  3 

Go  on  in  this  way  to  nineteen. 

What  does  the  figure  1  stand  for  in  the  number  12? 
In  the  number  13  ? 

In  14,  15,  16,  17,  18,  19  ? 

How  many  tens  in  11  ?     How  many  over  ? 

In  12,  13,  14,  15,  16,  17,  18,  19  ?  ' 

4.  Suppose  we  wish  to  write  the  number  ten.     We 
will  use  1  to  stand  for  ten  the  same  as  in  the  other 
numbers. 

How  many  will  there  be  over? 

What    shall    we   use  to    show    that  jj 
there  is  none  over  ?  * 

We  will  use  this  figure,   0.     Thus,  I  0 

The  figure,  0,  is  called   naught,  and  is  used  where 
nothing  belongs. 


6 


PRIMARY   ARITHMETIC 


Take  two  tens.  How  many  sticks  in  all  ? 
To  write  twenty  we  use  2  to  stand  for  two  tens, 
and  0  to  show  that  there  is  none  over,  thus, 

Take  two  tens  and  one,  thus, 

How  many  ?     Write  it  thus, 

m 
Make  the  figures  for:       jj 


0 


5.   In  the  same  manner  as  in  the  preceding  lesson,  develop 
numbers  to  one  hundred. 

Write  fifteen  ;  twenty ;  eighteen ;  fourteen. 
Write  twenty-five  ;  thirty-seven  ;  forty. 
Write  eighty-twro  ;  ninety-six  ;  seventy. 
Write  sixty-one  ;  forty-seven  ;  fifty. 
Write  seventy-nine  ;  twenty-one  ;  ninety. 
Write  forty-eight ;  nineteen  ;  thirty-three. 
Lay  counters  to  make  forty-two,  thus, 
Lay  counters  to  make  sixty-three. 
Lay  counters  to  make  seventeen. 
Count  the  desks  in  your  room. 


What  number  will  the  counters  on  the  table  make  ? 


PRIMARY   ARITHMETIC  7 

Count  the  hands  in  your  schoolroom. 
Write  the  number  of  books  on  the  teacher's  desk. 
Count  fifty  forward  and  backward. 
Read  these  numbers  :    25,  21,  38,  45,  36,  28,  72,  64. 
Write  them  in  a  column,  so  that  the  tens  will  be  in  a 
vertical  line. 

Write  them  in  words. 

ADDITION 

'6.    Take  one  counter. 

Take  one  more  counter. 

How  many  counters  have  you  ? 

How  did  you  get  two  counters  ? 

One  counter  and  one  counter  are  how  many  counters  ? 

One  stick  and  one  stick  are  how  many  sticks  ? 

One  book  and  one  book  are  how  many  books  ? 

One  boy  and  one  boy  are  how  many  boys  ? 

One  and  one  are  how  many  ? 

•    and    •    are    ? 

One  and  one  are    ? 

1     and    1    are    ? 

Write,  1  and  1  are  2. 

Take  two  counters. 

Put  one  more  with  them. 

How  many  counters  are  there  ? 

How  did  you  get  three  counters  ? 

Two  counters  and  one  counter  are  how  many  counters  ? 


PRIMARY  ARITHMETIC 


If  the  apples  in  the  boy's  hand  be  put  with  the  apple 
on  the  table,  how  many  will  there  be  on  the  table  ?  If 
the  one  book  be  put  on  the  three  books,  how  many 
books  will  there  be  in  the  pile  ? 

Make  a  number  story  about  the  two  books  and  one 
book. 

Make  a  number  story  about  the  apples  in  the  basket 
and  the  apple  on  the  table.  About  one  marble  and  one 
marble. 

Two  chairs  and  one  chair  are  how  many  chairs  ? 

Two  and  one  are  how  many  ? 

•  •     and    *   are    ? 

Two    and  one  are    ? 

2        and    1    are    ? 


PRIMARY   ARITHMETIC 


9 


In  the  same  way  teach  three  and  one,  four  and  one,  and  so  on 
to  ten  and  one. 

Have  children  write : 


1 

and 

1 

are 

2 

1 

+  1 

=    2 

2 

and 

1 

are 

3 

2 

+  1 

=    3 

3 

and 

1 

are 

4 

3 

+  1 

=   4 

4 

and 

1 

are 

5 

4 

+  1 

=    5 

5 

and 

1 

are 

6 

5 

+  1 

=    6 

6 

and 

1 

are 

7 

6 

+  1 

=    7 

7 

and 

1 

are 

8 

7 

4-1 

*    8 

8 

and 

1 

are 

9 

8 

4-1 

=    9 

9 

and 

1 

are 

10 

9 

+  1 

=  10 

10 

and 

1 

are 

11 

10 

+  1 

=  11 

BLACKBOARD  DRILL 

Add    the    1    to    each    of   the    other 
numbers  around  the  circle. 


7.    Take  1  counter.     Take  two  more  counters. 

How  many  counters  have  you  ? 

How  did  you  get  three  counters  ? 

One  counter  and  two  counters  are  how  many  counters  ? 

One  apple  and  two  apples  are  how  many  apples  ? 

One  and  two  are  how  many  ? 

Take  two  counters.     Take  two  more  counters. 

How  many  counters  have  you? 


10 


PRIMARY    ARITHMETIC 


How  did  you  get  four  counters  ? 

Two  counters  and  two  counters  are  how  many 
counters  ? 

Two  boards  and  two  boards  are  how  many  boards  ? 

Two  sheep  and  two  sheep  are  how  many  sheep  ? 

Two  and  two  are  how  many  ? 

Take  three  counters.     Take  two  more  counters. 

How  many  counters  have  you  ? 

How  did  you  get  five  counters  ? 

Three  counters  and  two  counters  are  how  many 
counters  ? 

Three  books  and  two  books  are  how  many  books  ? 

Three  trees  and  two  trees  are  how  many  trees  ? 

Three  and  two  are  how  many  ? 


In  a  similar  way  teach  the  entire  table  of  twos. 
Have  children  write : 


1 

and 

2 

are 

3 

1 

+  2 

=    3 

2 

and 

2 

are 

4 

2 

+  2 

=    4 

3 

and 

2 

are 

5 

3 

_l_  2 

=    5 

4 

and 

2 

are 

6 

4 

_l_  2 

=    6 

5 

and 

2 

are 

7 

5 

+  2 

=    7 

6 

and 

2 

are 

8 

6 

i  2 

=    8 

7 

and 

2 

are 

9 

7 

i  2 

Q 

8 

and 

2 

are 

10 

8 

_j_  2 

=  10 

9 

and 

2 

are 

11 

9 

+  2 

=  11 

10 

and 

2 

are 

12 

10 

_j_  2 

=  12 

PRIMARY   ARITHMETIC  11 


Make  a  number  story  about  3  dolls  and  2  dolls. 
Another  child  give  the  answer. 

Make  a  number  story  about  7  red  roses  and  2  white 
roses.  Give  the  answer. 

Make  a  story  about  6  and  2,  7  and  2,  etc. 


•   •••••   and   •   •   are    ? 

Six  and    two    are    ? 

6  +       2       =     ? 

c^  ^ ^ 

V^^       ^V  BLACKBOARD  DRILL 

b(        C\          \ 
)        LL        Add  the  2  to  each  of  the  other  num- 
^  ^  T4 

T 


\  /        bers  quickly. 

/  ^- ^o 


I 


8.    Take  1  counter.     Take  3  more  counters. 

How  many  counters  have  you  ? 

How  did  you  get  4  counters  ? 

One  counter  and  three  counters  are  how  many 
counters? 

One  stick  and  three  sticks  are  how  many  sticks  ? 

One  marble  and  three  marbles  are  how  many  mar- 
bles? 

One  cat  and  three  cats  are  how  many  cats  ? 

One  and  three  are  how  many  ? 

Take  two  counters.     Take  three  more  counters. 

How  many  counters  have  you  ? 

How  did  you  get  five  counters  ? 


12 


PRIMARY   ARITHMETIC 


Two    counters    and   three    counters    are   how  many 
counters  ? 

•   •  and  •   •   •  are  how  many  dots  ? 

Two  cows  and  three  cows  are  how  many  cows  ? 

Two  and  three  are  how  many  ? 

In  a  similar  ,way,  teach  all  the  table  of  threes. 

Make  a  number  story  about  2  red  cherries  and  3  red 
cherries.     Another  child  give  the  answer. 

Make  a  story  about  8  green  leaves  and  2  green  leaves. 

Make  a  number  story  about  2  boys  and  5  boys. 

Make  a  number  story  about  7  dollars  and  3  dollars. 
About  9  and  3. 

Have  children  write : 


1 

and 

3 

are 

4 

1 

+  3  = 

4 

2 

and 

3 

are 

5 

2 

1      O 

-f-  o  — 

5 

3 

and 

3 

are 

6 

3 

+  3  = 

6 

4 

and 

3 

are 

7 

4 

4-3  = 

7 

5 

and 

3 

are 

8 

5 

+  3  = 

8 

6 

and 

3 

are 

9 

6 

+  3  = 

9 

7 

and 

3 

are 

10 

7 

+  3  = 

10 

8 

and 

3 

are 

11 

8 

+  3  = 

11 

9 

and 

3 

are 

12 

9 

+  3  = 

12 

10 

and 

3 

are 

13 

10 

4-3  = 

13 

In  a  similar  manner  teach  the  entire  table  of  Addition,  giving 
much  drill  with  both  concrete  and  abstract  work,  as  you  proceed, 
to  fix  the  tables  in  the  minds  of  the  children. 

Vary  the  work,  sometimes  the  teacher  doing  the  work  and 
pupil  telling  what  she  did,  and  the  result. 

Have  children  make  questions. 


PRIMARY   ARITHMETIC 


13 


9. 


BLACKBOARD  DRILL 

Add  the  3  to  each  of  the  other  num- 
bers quickly. 

TABLE  OF  ADDITION 


1+1=  2 

1+2=  3 

1+3=  4 

1+4=  5 

1+  5=  6 

2  +  1=  3 

2+2=  4 

2+3=  5 

2+4=  6 

2+  5=  7 

3  +  1=  4 

3+2=  5 

3+3=  6 

3+4=  7 

3+  5=  8 

4  +  1=  5 

4+2=  6 

4+3=  7 

4+4=  8 

4+  5=  9 

5  +  1=  6 

5  +  2=  7 

5  +  3=  8 

5  +  4=  9 

5+  5=10 

6+1=  7 

6+2=  8 

6+3=  9 

6+4=10 

6+  5  =  11 

7  +  1=  8 

7  +  2=  9 

7+3=10 

7+4  =  11 

7+  5  =  12 

8  +  1=  9 

8+2=10 

8+3  =  11 

8+4  =  12 

8+  5=13 

9  +  1  =  10 

9+2=11 

9+3  =  12 

9  +  4=13 

9+  5=14 

io+i=n 

10+2  =  12 

10+3  =  13 

10+4=14 

10+  5=15 

1  +  6=  7 

1  +  7=  8 

1+8=  9 

1  +  9  =  10 

1+10=11 

2+6=  8 

2+7=  9 

2+8=10 

2+9  =  11 

2+10=12 

3+6=  9 

3+7  =  10 

3+8  =  11 

3  +  9  =  12 

3  +  10=13 

4+6=10 

4  +  7=11 

4+8=12 

4  +  9  =  13 

4+10=14 

5  +  6  =  11 

5+7=12 

5+8  =  13 

5+9  =  14 

5+10=15 

6+6  =  12 

6  +  7  =  13 

6+8  =  14 

6+9  =  15 

6+10=16 

7  +  6  =  13 

7  +  7  =  14 

7  +  8  =  15 

7  +  9  =  16 

7  +  10=17 

8  +  6  =  14 

8+7  =  15 

8+8=16 

8  +  9  =  17 

8  +  10  =  18 

9  +  6  =  15 

9  +  7  =  16 

9  +  8  =  17 

9+9=18 

9+10=19 

10  +  6  =  16 

10  +  7  =  17 

10  +  8  =  18 

10+9  =  19 

10  +  10=20 

14  PRIMARY   ARITHMETIC 

Give  three  answers  to  each  question  below : 


1.  ?- 

h? 

=  10 

9. 

9  _ 

f-? 

=  12 

2.   ?H 

h? 

=  17 

10. 

9  _ 

h? 

=  15 

3.   ?H 

h  ? 

=    9 

11. 

9  _ 

h? 

=  21 

4.   ?- 

h? 

=  20 

12. 

9  _ 

h? 

=  11 

5.   ?H 

-? 

=  14 

13. 

9  _ 

h? 

=    8 

6.   ?H 

_  9 

rr 

14. 

?- 

h? 

=    6 

7.    ?H 

_  9 

=  16 

15. 

?- 

h? 

=  18 

8.    ?H 

_  9 

=  13 

16. 

?H 

h? 

=  19 

ADDITION  DRILL  CHART 

This   chart  contains  all   additions   which   result  in  sums   no 
larger  than  20.      It  should  be  copied  on   the   blackboard,  and 


6 

5 

6 

10 

2 

8 

3 

3 

2 

'7 

7 

7 

1 

5 

4 

2 

4 

1 

9 

1 

5 

7 

2 

4 

5 

10 

4 

3 

6 

7 

10 

5 

2 

5 

7 

3 

2 

4 

4 

4 

3 

1 

5 

6 

8 

6 

2 

3 

2 

1 

10 

4 

6 

7 

8 

3 

1 

9 

3 

8 

1 

3 

1 

6 

1 

9 

9 

4 

6 

9 

2 

10 

8 

6 

9 

10 

3 

1 

5 

3 

5 

7 

8 

1 

8 

6 

5 

2 

10 

2 

10 

8 

9 

4 

10 

7 

8 

7 

10 

9 

4 

10 

5 

9 

9 

6 

9 

8 

8 

7 

children  should  recite  the  sums  every  day  until  they  can  do  so 
without  making  an  error.     Vary  the  drill.     Begin   at  different 


PRIMARY   ARITHMETIC 


15 


places  and  go  through  the  entire  chart  to  the  place  of  beginning. 
Change  the  order,  going  sometimes  to  right,  and  to  left,  and  some- 
times up -or  down.     Vary  concert  and  individual  recitation  with 
and  without  the  pointer.     Sometimes  pupils  use  the  pointer. 
Use  the  chart  persistently. 

10.    To  THE  TEACHER.    Pupils  need  drill  on  this  kind  of  work 
till  they  can  give  results  instantly. 


1 .  How  many  boys  are  5  boys  and  3  boys  ? 

2.  Three  eggs  and  4  eggs  are  how  many  eggs  ? 


16  PRIMARY   ARITHMETIC 

3.  How  many  are  six  tops  and  3  tops  ? 

4.  How  many  are  8  hens  and  7  hens  ? 

5.  Two  cats  and  four  cats  are  how  many  cats  ? 

6.  Five    books    and    two    books    are    how    many 
books  ? 

7.  Four  hats  and  six  hats  are  how  many  hats  ? 

8.  Eight  slates  and  nine  slates  are  how  many? 

9.  3  chairs  and  5  chairs  are  how  many  chairs  ? 

10.  Six  balls  and  three  balls  are  how  many  balls  ? 

11.  Five  and  two  are  how  many  ? 

12.  Nine  and  three  are  how  many  ? 

13.  How  many  are  four  and  four? 

14.  May  had  three  cents,  and  I  gave  her  8  cents ; 
how  many  cents  did  she  have  then  ? 

15.  John  found  4  eggs  in  one  nest  and  six  in  another ; 
how  many  eggs  did  he  find  ? 

16.  James  had  7  cents  and  found  4  more  ;  how  many 
cents  did  he  then  have  ? 

17.  Make  a  number  story  about  3  birds  and  6  birds. 
4  men  and  6  men.     5  and  2. 

11.    1.    A  boy  saw  6  squirrels  in  one  tree  and  4  in 
another.     How  many  squirrels  did  he  see  ? 

2.  5  oranges  +  3  oranges  =  ?       7  pins  +  9  pins  =  ? 
6  +  7  =  ? 

3.  Henry  had  5  cents,  John  4,  and  George  8.     How 
many  cents  did  they  all  have  ? 

4.  A  wagon  carried  7  women,  5  men,  and  3  chil- 
dren.    How  many  persons  did  it  carry? 


PRIMARY   ARITHMETIC 


17 


5. 

3+2+4=? 

22. 

8  +  5  =  ? 

6. 

2+7+5=? 

23. 

3+8+1+1=? 

7. 

4+8+2=? 

24. 

4+6+9=? 

8. 

6+5+3=? 

25. 

2+3+6+4=? 

9. 

9+2+5=? 

26. 

8+2+2+6=? 

10. 

6+1+4=? 

27. 

18  +  3  =  ? 

11. 

6+1+5=? 

28. 

28  +  3  =  ? 

12. 

5+6+1=? 

29. 

48  4-  3  =  ? 

13. 

7  +  24-8  =  ? 

30. 

69  +  5  =  ? 

14. 

l4_2  +  3  +  9  =  ? 

31. 

49  4.  10  +  1  =  ? 

15. 

6+3+1+8=? 

32. 

95  +  5  =  ? 

16. 

1+2+4+8=? 

33. 

7  4.  8  +  5  =  ? 

17. 
18. 
19. 
20. 

l4_9  +  2  +  l  =  ? 
54-2  +  3  +  9  =  ? 
6+4+8=? 
6+3+4=? 

34. 
35. 

Add  by  fives  from 
0  to  20. 
Add     by    threes 
from  0  to  30. 

21. 

6+1+6+2=? 

36.  Count  by  2's  from  0  to  40. 

37.  Count  by  4's  from  0  to  40. 

38.  Count  by  6's  from  0  to  48. 

39.  Count  by  7's  from  0  to  35. 

40.  Count  by  8's  from  0  to  48. 


From  1  to  21. 
From  2  to  30. 
From  5  to  42. 
From  5  to  47. 
From  6  to  54. 
5 


41.  Make    a    number    story    about    5    swallows,    9 
swallows,  and  3  swallows. 

«. 

42.  Make  a  number  story  about  5,  3,  and  8. 

12.    1.    Eight  boys  and  5  boys  are  how  many  boys? 
2.    Seven  eggs  and  three  eggs  are  how  many  eggs? 


18 


PRIMARY  ARITHMETIC 


3.  9  tops  and  three  tops  are  how  many  tops? 

4.  6  cats  and  2  cats  are  how  many  cats  ? 

5.  7  books  and  5  books  are  how  many  books  ? 

6.  10  hats  and  4  hats  are  how  many  hats  ? 

7.  10  slates  and  1  slate  are  how  many  slates  ? 

8.  How  many  chairs  are  8  chairs  and  3  chairs? 

9.  How  many  balls  are  10  balls  and  6  balls? 

10.  How  many  dogs  are  6  dogs  and  5  dogs? 

11.  11  days  and  4  days  are  how  many  days? 

12.  Seven  apples  and  4  apples  are  how  many  apples? 

13.  11  balls  and  5  balls  are  how  many  balls? 

14.  8  cows  and  3  cows  are  how  many  cows  ? 

15.  11  and  5  are  how  many? 

16.  10  and  four  are  how  many? 

17.  How  many  are  11  and  6  ? 

18.  John  spent  3  cents  for  candy,  5  cents  for  a  top, 
and  6  cents  for  marbles.     How  much  did  he  spend  in  all  ? 

19.  A  man  had  three  cows  in  one  field,  four  in  an- 
other, and  seven  in  another.     How  many  did  he  have  in 
all  ?  Make  a  picture  of  the  fields  using  dots  for  cows. 


20.   9  -f  4  =  ? 

28.   5+    7  =  ? 

36.   7  +  9  =  ? 

21.    8  +  5  =  ? 

29.   4+    8  =  ? 

37.   8  +  10  =  ? 

22.   6  +  2  =  ? 

30.   4+    9  =  ? 

38.   2  +  5  +  3  =  ? 

23.   9  +  2  =  ? 

31.   5  +  10  =  ? 

39.   4  +  6  +  7  =  ? 

24.    6  +  2  =  ? 

32.   8+    5  =  ? 

40.    9  +  1  +  5  =  ? 

25.    6  +  3  =  ? 

33.   9+    6  =  ? 

41.    8  +  2  +  3  =  ? 

26.   9  +  4  =  ? 

34.   8+    7  =  ? 

42.    9  +  9  +  2  +  1  =  ? 

27.    5  +  5  =  ? 

35.   8+    8  =  ? 

43.    1+2+3+4  +  5  =  ? 

PRIMARY  ARITHMETIC  19 


13.  1.  George  picked  O  O  Q  ^rom  on^  tree> 
O  C  O  O  O  from  another  tree,  and  Q  Q  Q 
O  O  O  fr°m  an°ther  tree.  How  many  did  he  pick 
in  all? 

2.    There    were 


one  row,  4  in  another,  and  9  in  another.     How  many 
trees  were  there  in  all  ? 

3.  A  girl  earned  8  cents,  found   5  cents,  and   had 

3  cents  given  to  her.     How  many  cents  had  she  ? 

4.  A   cat    caught     X^X^fe  V^Xjf*'     in   the 

and     %^%/%/%/%/^%/<%/   in 

the  field.     How  many  did  she  catch  in  all  ? 

5.  A  gardener  gave  Ned    ^  ^  ^  £},  Nell  K  K 

[X)  ^),  and  Will  as  many  as  the  other  two.      How 
many  fVs  did  he  give  all  ? 

6.  Frank  ate  three  plums,  gave  Charles  nine,  and 
had  four  left.     How  many  plums  had  he  at  first  ? 

7.  I  saw  on  the  lawn    10  sparrows,  6    robins,  and 

4  orioles.     How  many  birds  did  I  see  in  all  ? 

8.  A  boy  paid    2  dollars    for  shoes,  1  dollar  for  a 
hat,  5  dollars  for  a  coat,  and  9  dollars  for  books.     How 
much  did  he  pay  for  all  ? 

9.  A  boy  caught  10  fish,  and    his    sister  9.     How 
many  fish  did  both  catch? 


20  PRIMARY   ARITHMETIC 

10.  Nancy  walked  2  miles  on  Monday,  3  miles  on 
Wednesday,  4  miles  on  Thursday,  and  9  miles  on  Sat- 
urday.    How  far  did  she  walk  ? 

11.  1  +  2  +  3  +  4  +  5  =  ?  16.  7  +  7  +  6  =  ? 

12.  2  +  1  +  9  =  ?  17.  12  +  8  =  ? 

13.  10  +  10  =  ?  18.  5  +  1  +  6  +  3  =  ? 

14.  4  +  8  +  2  =  ?  19.  3  +  4  +  5  =  ? 

15.  9  +  1  +  6  =  ?  20.  6  +  9  =  ? 

SUBTRACTION 

14.  Teacher  take  two  counters,  and  children  tell 
how  many.  Teacher  take  one  away,  and  children  tell 
what  she  has  done,  and  how  many  are  left. 

Children  take  two  counters,  take  one  away,  and  tell 
how  many  are  left. 

Two  counters  less  one  counter  are  how  many 
counters  ? 

Two  boxes  less  one  box  are  how  many  boxes  ? 

Two  knives  less  one  knife  ? 

Two  flowers  less  one  flower  ? 

Two  less  one  are  how  many  ? 

Teacher  take  three  counters,  and  children  tell  how 
many.  Teacher  take  one  away,  and  children  tell  what 
she  did,  and  number  left. 

Three  counters  less  one  counter  are  how  many 
counters  ? 

Three  books  less  one  book  are  how  many  books  ? 

Three  less  one  are  how  many  ? 


PRIMARY   ARITHMETIC 


21 


O  O  less  O 

Three  less  one  are 
3       less     1     are 


So  on  till  all  the  ones  are  taught. 
Children  write : 


2 

less 

1 

are 

1 

2- 

1  = 

1 

3 

less 

1 

are 

2 

3- 

1  = 

2 

4 

less 

1 

are 

3 

4- 

1  = 

3 

5 

less 

1 

are 

4 

5- 

1  = 

4 

6 

less 

1 

are 

5 

6- 

1  = 

5 

7 

less 

1 

are 

6 

7  — 

1  = 

6 

8 

less 

1 

are 

7 

8- 

1  = 

7 

9 

less 

1 

are 

8 

9- 

-j  

8 

10 

less 

1 

are 

9 

10- 

1  = 

9 

11 

less 

1 

are 

10 

11- 

1  = 

10 

I 

Make  a  number  story 
about  the  holly  leaves. 
Give  the  answer. 

Make  an  adding  story 
about  the  holly  buds. 
Give  the  answer. 

Make    a    number    story 
about  a  tree,  9  blackbirds, 
and    1   blackbird. 
Make  a  number  story  about  8  and  1. 


PRIMARY   ARITHMETIC 


BLACKBOARD  WORK 

Take   one  from  each   of   the   other 

numbers, 
o 


15.  Teacher  take  three  counters,  and  children  tell 
how  many. 

Take  away  two  counters.  Children  tell  what  has 
been  done  and  how  many  are  left. 

Children  take  three  counters.  Take  away  two 
counters.  Tell  what  has  been  done,  and  how  many 
are  left. 

Three  counters  less  two  counters  are  how  many 
counters  ? 

Three  peaches  less  two  peaches  are  how  many 
peaches  ? 

Three  less  two  are  how  many  ? 

Teacher  take  four  counters.  Take  away  two  counters. 
How  many  are  left  ?  Children  tell  what  has  been  done, 
and  the  result. 

Teacher  take  five  counters ;  take  away  two.  Chil- 
dren watch  carefully  and  tell  the  whole  story  —  what 
has  been  done  and  the  result. 

OOOOO   less    CO   are     ? 
Five  less  two  are     ? 

5       -      2      =      ? 


PRIMARY   ARITHMETIC 


23 


How  many  oranges  on  the  plate  in  the  picture  ? 
If   the  girl  takes  away  2  oranges,  how  many  will 
be  left? 

Five  less  two  are  how  many  ? 

So  on  through  the  remainder  of  table  of  twos. 
Children  write : 


3 

less 

2 

are 

1 

3 

_  2  — 

1 

4 

less 

2 

are 

2 

4 

—  2  = 

2 

5 

less 

2 

are 

3 

5 

_  0  

3 

6 

less 

2 

are 

4 

6 

—  2  = 

4 

7 

less 

2 

are 

5 

7 

-2  = 

5 

8 

less 

2 

are 

6 

8 

2  

6 

9 

less 

2 

are 

7 

9 

-2  = 

7 

10 

less 

2 

are 

8 

10 

2  = 

8 

11 

less 

2 

are 

9 

11 

-2  = 

9 

12 

less 

2 

are 

10 

12 

o  

10 

24  PRIMARY  ARITHMETIC 

Make  a  number  story  about  a  pond,  a  bank,  9  ducks, 
and  2  ducks.     Give  the  answer. 

Make  a  number  story  about  8  less  2. 


BLACKBOARD  WORK 

Take  2  from  each  of  the  other  num- 
bers. 


16.    Children  watch. 

Teacher  take  four  counters,  and  take  away  three. 

Children  tell  what  is  done,  and  the  result. 

Four  counters  less  three  counters  are  how  many 
counters  ? 

Four  roses  less  three  roses  ? 

Four  hats  less  three  hats  ? 

Four  less  three  ? 

Children  watch. 

Teacher  take  five  counters,  and  take  away  three. 

Children  do  just  what  teacher  has  done,  tell  what 
they  have  done,  and  the  result. 

Five  less  three  are  how  many  ? 

So  on  until  all  the  threes  have  been  taught. 

Make  a  number  story  about  9  eggs,  a  nest,  and  3 
eggs.  Give  the  answer. 

Make  a  story  about  12  less  3. 

Children  write  the  table  of  threes  as  in  previous  lessons. 


PRIMARY   ARITHMETIC  25 

' 

1.  Mary  had  9  roses,  and  gave  Helen  3.    How  many 
roses  had  she  left  ? 

NOTE.  —  If  a  child  fails,  let  him  take  9  counters,  call  them  roses; 
take  away  three  "  roses,"  and  see  how  many  roses  are  left. 

2.  George  earned  5  cents,  and  spent  3  cents.     How 
many  cents  had  he  left  ? 

3.  Seven   quarts  of    water  were   in  a  pail.     Three 
quarts  leaked  out.     How  many  were  left  ? 

4.  Henry  has  7  cents.     How  much  must  he  earn  to 
buy  a  ball  for  10  cents  ? 

5.  Make  a  question  that  has  3  for  an  answer. 

II 

BLACKBOARD  DRILL 

Subtract  3  from  each  of  the  other 
numbers  around  the  circle. 

In  a  similar  way  teach  all  the  table  of  subtraction.     Show 
with  counters  that  2-2  =  0,  ^-3  =  0,  4-4  =  0,  5-5  =  0. 

17.  TABLE  OF  SUBTRACTION 


1-1=  0 

2-2=  0 

3-3=  0 

4-4=  0 

5-5=  0 

2-1  =  1 

3-2=  1 

4-3=  1 

5-4=  1 

6-5=  1 

3-1=  2 

4-2=  2 

5-3=  2 

6-4=  2 

7-5=  2 

4-1=  3 

5-2  =  .  3 

6-3=  3 

7-4=  3 

8-5=  3 

5-1=  4 

6-2=  4 

7-3=  4 

8-4=  4 

9-5=  '4 

6-1=  5 

7-2=  5 

8-3=  5 

9-4=  5 

10-5=  5 

7-1=  6 

8-2=  6 

9-3=  6 

10-4=  6 

11-5=  6 

8-1=  7 

9-2=  7 

10-3=  7 

11-4=  7 

12-5=  7 

9-1=  8 

10-2=  8 

11-3=  8 

12-4=  8 

13-5=  8 

10-1=  9 

11-2=  9 

12-3=  9 

13-4=  9 

14-5=  9 

11-1  =  10 

12-2  =  10 

13-3=10 

14-4  =  10 

15-5  =  10 

26 


PRIMARY    ARITHMETIC 


TABLE  OF  SUBTRACTION  (Continued) 


6-6=  0 

7-7  =  0 

8-8=  0 

9-9=  0 

10-10=  0 

7-6=  1 

8-7=  1 

9-8=  1 

10-9=  1 

11-10=  1 

8-6=  2 

9-7=  2 

10-8=  2 

11-9=  2 

12-10=  2 

9-6=  3 

10-7=  3 

11-8=  3 

12-9=  3 

13-10=  3 

10-6=  4 

11-7=  4 

12-8=  4 

13-9=  4 

14-10=  4 

11-6=  5 

12-7=  5 

13-8=  5 

14-9=  5 

15-10=  5 

12-6=  6 

13-7=  6 

14-8=  6 

15-9=  6 

16-10=  6 

13-6=  7 

14-7=  7 

15-8=  7 

16-9=  7 

17-10=  7 

14-6=  8 

15-7=  8 

16-8=  8 

17-9=  8 

18-10=  8 

15-6=  9 

16-7=  9 

17-8=  9 

18-9=  9 

19-10=  9 

16-6=10 

17-7  =  10 

18-8=10 

19-9=10 

20-10=10 

Give  three  answers  to  each  of  these  questions : 


1.   20-?  =  ? 

7.   14-?  =  ? 

13.   8-?  =  ? 

2.    19-?  =  ? 

8.   13-?  =  ? 

14.    7-?  =  ? 

3.   18-?  =  ? 

9.   12-?  =  ? 

15.    6-?  =  ? 

4.   17-?  =  ? 

10.   11-?*=? 

16.   5-?  =  ? 

5.   16_?  =  ? 

11.   10-?  =  ? 

17.   4-?  =  ? 

6.   15-?  =  ? 

12.   9-?  =  ? 

18.   3-?  =  ? 

SUBTRACTION  DRILL  CHART 

This  chart  contains  all  the  subtraction  table.  It  should  be 
copied  on  the  blackboard,  and  remainders  recited  by  the  class 
every  day  till  mastered.  Vary  the  drill.  Begin  sometimes  at 
the  upper  left-hand  corner,  sometimes  at  the  lower  right-hand 
corner.  Go  up  and  down,  to  the  right  and  the  left.  Recite 
sometimes  in  concert  and  sometimes  individually,  teacher  or 
pupil  using  the  pointer,  and  sometimes  without  the  pointer. 


PRIMARY   ARITHMETIC 


27 


11 

4 

15 

9 

13 

12 

6 

15 

11 

16 

-10 

-2 

-7 

-9 

-8 

-9 

-5 

-6 

-2 

-8 

9 

12 

13 

6 

11 

10 

19 

7 

6 

8 

-6 

-5 

-9 

-1 

-6 

-8 

-10 

-4 

-2 

-3 

8 

11 

7 

8 

9 

6 

11 

3 

3 

15 

-5 

g 

-3 

-6 

-3 

-3 

-5 

-2 

-1 

-8 

10 

13 

9 

14 

13 

9 

11 

10 

9 

5 

-6 

-5 

-7 

-6 

-7 

-1 

-8 

-7 

-8 

3 

14 

12 

11 

17 

6 

7 

2 

14 

8 

17 

-10 

-6 

-3 

-9 

-4 

-6 

—  2 

-8 

-5 

-10 

12 

10 

12 

12 

11 

7 

9 

5 

8 

17 

-3 

-1 

_  j 

-8 

-9 

-1 

-5 

-4 

-8 

-8 

9 

7 

8 

8 

4 

16 

18 

9 

4 

8 

-5 

-2 

-2 

—  7 

-3 

-10 

-10 

-2 

-1 

-1 

13 

15 

5 

10 

11 

i 

3 

13 

5 

16 

-6 

-9 

—  2 

-9 

-1 

-5 

-3 

-5 

_1 

—9 

14 

5 

7 

14 

12 

10 

12 

11 

16 

10 

-5 

—  5 

-7 

-9 

—5 

-5 

-10 

—  7 

-7 

-5 

10 

4 

10 

6 

14 

18 

15 

2 

13 

1 

-10 

-4 

-3 

-6 

—  7 

-9 

-10 

-1 

-10 

-1 

FOR  THE  TEACHER  :  —  After  a  table  has  once  been  developed, 
the  pupil  should  be  thoroughly  drilled  upon  it. 

Give  much  concrete  work.  In  drill  work,  do  not  allow  the 
child  to  use  counters  in  finding  the  answers,  but  require  him  to 
rely  upon  his  memory.  If  he  gives  a  wrong  answer,  he  should 
find  and  correct  his  error  by  means  of  the  counters. 


28 


PRIMARY   ARITHMETIC 


BLACKBOARD   DRILL 


15 


£0 


18.    1.     May  had  4  pictures  and  gave  away  2  of  them. 
How  many  had  she  left  ? 

2.  In  a  field  were  11  sheep.     The  dogs  killed  5  of 
them.     How  many  were  left  ? 

3.  In  a  class  were  9  scholars.     Four  of  them  were 
boys.     How  many  were  girls? 

4.  Henry  had  13  marbles.     He  lost  3  and  gave  away 
1.     How  many  had  he  left  ? 

5.  In  a  class  were  12  scholars.     Six  of  them  were 
girls.     How  many  were  boys  ? 

6.  The   number   of   boys   in   a  class  was  ten.     The 
number  of  girls  was  3   less.      How  many  girls  were 
there  ? 

7.  William  is  14  years  old.     James  is  nine.     Wil- 
liam is  how  much  older  than  James  ? 


PRIMARY   ARITHMETIC 


29 


8.  Celia  is  12  years  old.     Sarah  is  5  years  younger. 
How  old  is  Sarah  ? 

9.  A  farmer  planted  18  trees.     Ten  of  them  died. 
How  many  lived  ? 

10.  A  hen  hatched  11  chickens.  Two  of  them  were 
white  and  the  rest  speckled.  How  many  of  them  were 
speckled  ? 


11. 

13 

less 

6 

are 

9 

24. 

19 

—    9  = 

9 

12. 

12 

less 

5 

are 

9 

25. 

17 

-    8  = 

9 

13. 

9 

less 

5 

are 

9 

26. 

12 

rr  

9 

14. 

8 

less 

6 

are 

9 

27. 

12 

-    6  = 

9 

15. 

5 

less 

2 

are 

9 

28. 

14 

—    7  = 

9 

16. 

10 

less 

9 

are 

9 

29. 

18 

-    8  = 

9 

17. 

11 

less 

4 

are 

9 

30. 

17 

-    8  = 

? 

18. 

13 

less 

4 

are 

9 

31. 

18 

-    9  = 

9 

19. 

15 

less 

5 

are 

9 

32. 

11 

-    5  = 

9 

20. 

14 

less 

7 

are 

9 

33. 

12 

-    4  = 

9 

21. 

9 

less 

5 

are 

9 

34. 

15 

-    8  = 

9 

22. 

8 

less 

6 

are 

9 

35. 

20 

-10  = 

9 

23. 

9 

less 

5 

are 

9 

36. 

19 

9  _ 

9 

19.     1.    A  boy  had  5  cents  and  earned  7  cents  more. 
How  many  cents  did  he  then  have  ? 

2.  A  boy  had  15  cents  and  spent  10  cents.     How 
many  cents  had  he  left  ? 

3.  A  lady  had  7  pies  on  a  shelf  and  3  on  a  table. 
How  many  pies  had  she  ? 

4.  A  man  had  8  horses  and  bought  6  more.     How 
many  had  he  then  ? 


30  PRIMARY   ARITHMETIC 

5.  There  were  17  apples  in  a  dish.     A  boy  took  out 
9  of  them.     How  many  were  left  ? 

6.  I  had  9  dollars.      I  paid  5  dollars  for  a  chair 
and  the  rest  of  my  money  for  a  table.     What  did  the 
table  cost  ? 

7.  There  were  8  boys  in  a  chestnut  tree  and  7  on 
the  ground.     How  many  in  all? 

8.  Henry  had  5  books.     His  aunt  gave  him  3  and 
his  sister  4.     How  many  had  he  then? 

9.  Mary  is  15  years  old  and  John  is  5  years  younger. 
How  old  is  John  ? 

10.  Make  a  number  story  about  6  and  5. 

11.  Make  a  number  story  about  13  and  4. 

12.  Make  a  number  story  about  2  and  7. 

13.  Make  a  subtracting  story  about  hens. 

14.  Make  an  adding  story  about  birds. 

20.     1.    A  clerk  cut  10  yards  of  cloth  from  a  piece 
containing  19  yards.     How  many  yards  were  left  ? 

2.  Seven  ducks  came  to  a  pond;  then  8  more  came; 
then  6  flew  away.     How  many  were  left  ? 

3.  Robert  earned  6  cents  on  Monday,  4  cents  on 
Tuesday,  and  7  cents  on  Wednesday.     He  spent  9  cents 
on  Thursday.     How  much  had  he  left  ? 

4.  There  were    15    words    in    the   spelling  lesson. 
Richard  missed  4.     How  many  did  he  spell  right? 

5.  A  carpenter  cut  7  feet  from  a   16-foot  board. 
How  long  a  piece  was  left  ? 

6.  In  a  basket  were  5  red  plums,  5  green  ones,  and 
9  blue  ones.     How  many  were  there  ? 


PRIMARY   ARITHMETIC  31 

7.  A  boy  had  a  nickel  and  a  dime.     He  bought  a 
top  for  3  cents  and  some  buns  for  4  cents.     How  much 
money  had  he  left  ? 

8.  A  farmer  sold  some  wheat  for  10  dollars  and 
some  potatoes  for  7  dollars.     He  wanted  to  buy  some 
clothing  for  20  dollars.     How  much  more  money  did  he 
need  ? 

9.  A  boy  had   13   cents.     He   spent   6   cents  and 
earned  9  cents.     How  much  had  he  then  ? 

10.  Count  by  threes  from  2  to  23. 

11.  8  +  7  =  ?  18.    14-5  =  ? 

12.  15-8  =  ?  19.    14-9  =  ? 

13.  7  =  15-?  20.    9  +  ?=  14 

14.  18  =  9  +  ?  21.   2  +  4  +  7-8  +  3  =  ? 

15.  9  +  ?=18  22.    13-4-6  +  3  +  8  =  ? 

16.  9  +  9  =  ?  23.    1  +  2  +  3-3  +  7  +  9  =  ? 

17.  14  =  5  +  ?  24.    12  +  1  +  1  +  1-10  +  4  =  ? 
Count  by  2's  backward  from  28  to  0.     From  39  to  1. 
Count  by  5's  from  0  to  50,  and  back  again. 

Add  by  6's  from  0  to  54,  and  subtract  by  6's  back 
to  0. 

MULTIPLICATION 

21.    Take  one  counter. 

Take  one  more  counter. 

What  have  you  done  ? 

How  many  times  did  you  take  one  counter  ? 

Two  times  1  counter  are  how  many  counters  ? 

Two  times  1  stick  are  how  many  sticks  ? 


32 


PRIMARY   ARITHMETIC 


Two  times  1  boy  are  how  many  boys  ? 

Two  times  1  chair  are  how  many  chairs  ? 

Two  times  1  are  how  many  ? 

Take  one  counter.  Take  one  more  counter.  Take 
one  more  counter.  How  many  counters  have  you  ? 

What  did  you  do  to  get  3  counters  ? 

Three  times  1  counter  are  how  many  counters? 

Three  times  1  pencil  are  how  many  pencils  ? 

Three  times  1  day  are  how  many  days  ? 

Take  1  counter.  Take  1  more  counter.  Take  1  more 
counter.  Take  1  more  counter.  What  did  you  do  ? 
How  many  counters  have  you  ? 

Four  times  1  counter  are  how  many  counters  ? 

Four  times  1  star  are  how  many  stars  ? 

Four  times  1  leaf  are  how  many  leaves  ? 

Four  times  1  are  how  many  ? 

Similarly  teach  to  "  10  times  1  are  10." 
Have  children  write : 


2 

times 

1 

are 

2 

1 

X 

2  = 

2 

3 

times 

1 

are 

3 

1 

X 

o  

3 

4 

times 

1 

are 

4 

1 

X 

4  = 

4 

5 

times 

1 

are 

5 

1 

X 

5  = 

5 

6 

times 

1 

are 

6 

1 

X 

6  = 

6 

7 

times 

1 

are 

7 

1 

X 

7  = 

7 

8 

times 

1 

are 

8 

1 

X 

o  

8 

9 

times 

1 

are 

9 

1 

X 

9  = 

9 

10 

times 

1 

are 

10 

1 

X 

10  = 

10 

PRIMARY  ARITHMETIC  33 

22.    Lay  2  counters.     Lay  2  more  counters.     Thus, 


How  many  counters  have  you  ? 

What  did  you  do  to  get  four  counters  ? 

How  many  times  did  you  take  2  counters  ? 

Two  times  two  counters  are  how  many  counters  ? 

Two  times  2  dots  are  how  many  dots  ? 

Two  times  2  balls  are  how  many  balls  ? 

Two  times  2  are  how  many  ? 

Lay  2  counters.     Lay  2  more.     Lay  2  more.     Thus, 


How  many  counters  have  you  ? 

How  did  you  get  six  counters  ? 

Three  times  2  counters  are  how  many  counters  ? 

Three  times  2  pegs  are  how  many  pegs  ? 

Three  times  2  knives  are  how  many  knives  ? 

Three  times  2  are  how  many  ? 

Lay  2  counters,  2  more,  2  more,  2  more.    Thus, 


How  many  counters  have  you? 

How  did  you  get  eight  counters  ? 

Four  times  2  counters  are  how  many  counters? 

Four  times  2  bats  are  how  many  bats  ? 

Four  times  2  rabbits  are  how  many  rabbits  ? 

Four  times  2  are  how  many  ? 

Similarly  teach  the  rest  of  this  table. 


34 


PRIMARY  ARITHMETIC 


Children  write : 


2 

times 

2 

are 

4 

2 

X 

2 

=    4 

3 

times 

2 

are 

6 

2 

X 

3 

=    6 

4 

times 

2 

are 

8 

2 

X 

4 

-    8 

5 

times 

2 

are 

10 

2 

X 

5 

-10 

6 

times 

2 

are 

12 

2 

X 

6 

=  12 

7 

times 

2 

are 

14 

2 

X 

7 

-14 

8 

times 

2 

are 

16 

2 

X 

8 

=  16 

9 

times 

2 

are 

18 

2 

X 

9 

-18 

10 

times 

2 

are 

20 

2 

X 

10 

-20 

23.  1.  In  our  yard  are  3  trees,  and  2  birds  live  in 
each  tree.     How  many  birds  live  in  all  the  trees  ? 

2.  How  many  hands  have  4  boys  ? 

3.  How  many  thumbs  have  5  girls  ? 

4.  How  many  shoes  in  10  pair? 

5.  How  many  sleeves  are  there  in  7  coats  ? 

6.  How  many  noses  have  6  dogs  ? 

7.  How  many  eyes  have  6  sheep  ? 

8.  Make  a  story  about  3  pockets  and  2  cents. 

9.  Make  a  story  about  6  times  2  feet. 

10.  Make  a  story  about  8  times  2  gloves. 

11.  Make  a  story  about  9  windows  and  2  panes  of  glass. 


BLACKBOARD  DRILL 

Take  2  times  each  number  around 
the  circle. 


PRIMARY    ARITHMETIC 


35 


How  many  peaches  do  you  see  in  the  picture  ?  If 
the  boy  puts  all  of  the  peaches  into  the  dish,  taking 
two  at  a  time,  how  many  times  will  it  take  him  ? 

Make  a  number  story  about  the  books  on  the  table. 

24.  Teacher  lay  3  counters,  and  3  more  counters.  Children 
watch  and  tell  the  teacher  what  she  did  and  how  many  counters 
she  has. 

Two  times  3  counters  are  how  many  counters  ? 
Two  times  3  pegs  are  how  many  pegs  ? 
Two  times  3  sticks  are  how  many  sticks  ? 
Two  times  3  trees  are  how  many  trees  ? 
Two  times  3  are  how  many  ? 

In  the  same  way  teach  the  rest  of  this  table  to  "  10  times  3." 
Children  write  the  table  as  in  preceding  lesson. 


36  PRIMARY   ARITHMETIC 

v5 


BLACKBOARD  DRILL 

'"H       O       }*^       Find  3  times  each  of  the  numbers 
V  /       around  the  circle. 

\r\ 


1.  Two  girls  had  3  cents  apiece.     How  many  cents 
had  both  ? 

2.  Six  men  earn  three  dollars  a  day  apiece.     How 
many  dollars  do  all  earn  in  a  day  ? 

3.  Fred  has  9  three-cent  pieces.     How  much  money 
has  he  ? 

4.  There  are  3  feet  in  1  yard.     How  many  feet  in 
7  yards  ? 

5.  If  a  cord  of  wood  costs  3  dollars,  what  will  8 
cords  cost  ? 

6.  What  is  the  cost  of  4  pencils  at  3  cents  apiece  ? 

7.  How  far  can  you  walk  in  8  hours,  if  you  walk 
3  miles  every  hour  ? 

8.  If  it  takes  3  horses  to  draw  a  van,  how  many 
horses  can  draw  8  vans  ? 

9.  If  lemons  cost  4  cents  apiece,  what  will  3  lemons 
cost? 

10.    In  an  orchard  there  are  3  rows  of  trees  with  10 
trees  in  a  row.     How  many  trees  are  in  the  orchard  ? 

In  the  same  way  teach  the  remainder  of  the  multiplication 
table.     Give  much  concrete  work  after  each  part  of  the  table. 
Call  attention  to   1  x  0  =  0,  2  x  0  =  0,  3  x  0  =  0,  etc. 
Also,  1x1  =  1,  1x2-2,  1x3  =  3,  etc. 


PRIMARY   ARITHMETIC 


37 


25. 


TABLE  OF  MULTIPLICATION 


lx  1=  1 

2x   1=  2 

3x   1=  3 

4x   1=  4 

5x   1=     5 

Ix  2=  2 

2x   2=  4 

3x   2=  6 

4x   2=  8 

5x   2=  10 

lx  3=  3 

2x  3=  6 

3x  3=  9 

4x  3  =  12 

5x   3=  15 

lx   4  =  4 

2x  4=  8 

3x  4=12 

4x   4  =  16 

5x  4=  20 

lx   5=  5 

2x   5=10 

3x   5=15 

4x   5=20 

5x   5=  25 

lx   6=  6 

2x   6=12 

3x   6  =  18 

4x   6  =  24 

5x   6=  30 

lx   1=  1 

2x   7=14 

3x   7=21 

4x   7  =  28 

5x   7=  35 

lx   8=  8 

2x   8=16 

3x   8=24 

4x   8=32 

5x   8=  40 

lx   9=  9 

2x   9=18 

3x   9  =  27 

4x   9  =  36 

5x   9=  45 

1x10=10 

2x10  =  20 

3x10=30 

4x10  =  40 

5x10=  50 

6x   1=  6 

7x   1=  7 

8x   1=  8 

9x   1=  9 

10  x   1=  10 

6x  2-12 

7x  2  =  14 

8x  2  =  16 

9x   2=18 

10  x   2=  20 

6x  3-18 

7x   3=21 

8x   3=24 

9x   3  =  27 

10  x  3=  30 

6x   4=24 

7x  4=28 

8x   4=32 

9x  4=36 

10  x  4=  40 

6x  5=30 

7x   5=35 

8x   5=40 

9x   5=45 

10  x  5=  50 

6x   6=36 

7x   6=42 

8x   6=48 

9x   6=54 

10  x   6=  60 

6x   7=42 

7x   7=49 

8x   7=56 

9x   7=63 

10  x   7=  70 

6x   8=48 

7x   8  =  56 

8x   8  =  64 

9x   8  =  72 

iOx   8=  80 

6x   9  =  54 

7x   9=63 

8x   9=72 

9x   9=81 

10  x   9=  90 

6x10=60 

7x10=70 

8x10=80 

9x10=90 

10x10=100 

1. 

?x 

?  =  81 

2. 

?  x 

?=12 

(Two  answers) 

3, 

?x 

?  =  24 

(Two  answers) 

4. 

?x 

?  =  32 

5. 

?x 

?  =  20 

(Two  answers) 

6. 

?x 

?  =  16 

(Two  answers) 

7. 

?x 

?=18 

(Two  answers) 

8. 

?x 

?  =  25 

9. 

?x 

?=45 

10. 

?  X 

?  =  56 

11. 

?x 

?=63 

12. 

?  X 

?  =  90 

13. 

?x 

?=72 

14. 

?  X 

?  =  50 

15. 

?x 

?  =  21 

16. 

?x 

?  =  14 

17. 

?x 

?=35 

18. 

?x 

?  =  64 

19. 

?x 

?  =  40 

20.    ?x?  =  28 


38 


PRIMARY  ARITHMETIC 
MULTIPLICATION  DRILL  CHART 


This  chart  contains  all  combinations  of  two  factors  from  1  to 
10.  It  should  be  copied  on  the  blackboard,  and  the  products 
should  be  recited  daily  till  mastered.  Vary  the  drill  as  in  Sub- 
traction and  Addition.  Persist  in  the  use  of  the  chart. 


9 

5 

9 

3 

6 

rr 
i 

2 

7 

8 

9 

10 

3 

4 

7 

3 

4 

6 

2 

5 

1 

5 

2 

10 

7 

6 

3 

2 

4 

10 

3 

10 

8 

8 

7 

1 

5 

2 

1 

3 

5 

1 

8 

2 

8 

8 

8 

1 

5 

7 

10 

6 

10 

6 

4 

9 

3 

6 

1 

5 

2 

3 

2 

4 

3 

1 

2 

9 

6 

9 

9 

8 

5 

8 

7 

10 

9 

10 

8 

1 

9 

1 

7 

1 

5 

3 

6 

4 

9 

9 

8 

5 

6 

10 

7 

7 

4 

10 

5 

4 

6 

4 

2 

6 

1 

7 

4 

2 

10 

3 

4 

Occasionally  let  one  pupil  read  the  chart  aloud  from  the  book, 
using  the  upper  number  for  a  multiplier,  the  other  pupils  of  the 
class  giving  the  products. 

26.    Drill  on  the  table  of  multiplication. 

If  a  pupil  gives  a  wrong  answer,  let  him  find  and  correct  his 
mistake  by  means  of  counters. 

1.  What  will  10  oranges  cost  at  5  cents  apiece?     7 
lemons  at  3  cents?     6  tops  at  8  cents?     9  sleds  at  4 
dollars  ? 

2.  Six  boys  each  picked  7  quarts  of  berries.     How 
many  quarts  did  all  pick  ? 

3.  A  newsboy  made  5  cents  a  day  for  9  days.     How 
much  did  he  make  ? 


PRIMARY   ARITHMETIC  *   i          39 

^sL£*  u  F  o  tyiiJX^ 

'  ^^^^BBHMBHI^^'^^ 

4.  How  much  could  a  newsboy  make  in  5  days,  at 
9  cents  a  day  ?     In  8  days,  at  1 0  cents  a  day  ?     In  3 
days,  at  7  cents  a  day  ? 

5.  A    dime    is    10   cents.     How  many  cents    in    2 
dimes  ?     In  4  dimes  ?     In  5  dimes  ?     In  7  dimes  ?     In 
9  dimes  ? 

6.  Which  is  greater,  9  times  8,  or  8  times  9  ? 

7.  A  man  has  4  fields  of  corn,  and  4  men  work  in 
each  field.     How  many  men  in  all  the  fields  ? 

8.  A  lady  has  5  boxes,  with  6  spoons  in  each  box. 
How  many  spoons  has  she  ? 

9.  Write  the  table  of  8's,  9's,  7's,  5's,  6's,  4's. 

10.  At  10  cents  a  dozen,  what  will  8  dozen  bananas 
cost? 

11.  How  many  wings  have  5  birds  ? 

12.  Rose  has  8  marbles,  and  her  brother  7  times  as 
many.     How  many  has  her  brother  ? 

13.  If  there  are  9  plants  each  in  5  rows,  how  many 
plants  in  all  ? 

14.  If  a  dozen  eggs  cost  12  cents,  what  will  10  dozen 
cost? 

15.  Harry  can  pick  4  quarts  of  berries  in  one  day. 
At  the  same  rate,  how  many  can  he  pick  in  10  days  ? 


Make  stories  about  this  picture. 

Make  a  picture  of  5  squares  in  6  rows,  and  tell  a 
number  story  about  it. 


40 


PRIMARY  .ARITHMETIC 
BLACKBOARD  DRILL 


Multiply  the  figure  in  the  centre  of  each  circle  by  the  different 
numbers  around  it.     Answers  should  be  instantaneous. 


10 


3 


27.    Addition,  Subtraction,  and  Multiplication. 

1.  A  man  saw  4  ducks  in  one  pond,  5  in  another, 
and  7  in  another.     How  many  ducks  did  he  see  ?     Make 
a  picture. 

2.  A  man  picked  six  pears  from  one  tree,  six  from 
another,  and  five  from  another.     How  many  pears  did 
he  pick  ? 

3.  Suppose    each    of    these    dots    is    a    tree.      How 
many  rows  of  trees  are   there  ?     How    •••••••• 

many    trees    in    a    row  ?      How   many 

trees   in  the    orchard  ?      How   do  you    •  ••••••• 

find  it  ?  '  •  •  • 


PRIMARY  ARITHMETIC  41 

4.  Make  an  orchard  of  3  rows,  with  9  trees  in  a 
row.     Howr  many  trees  in  the  orchard  ? 

5.  Make  an  orchard  of  4  rows,  with  7  trees  in  a 
row.     How  many  trees  in  the  orchard? 

6.  Nelly  had  11  apples  arid  gave  away  5.     How 
many  had  she  left  ? 

7.  Make  a  story  about  3  apples,  4   apples,  and  7 
apples. 

8.  Will's  father  gave  him  20  cents.      He  paid  five 
cents  for  a  tablet  and  5  cents  for  a  pencil.     How  much 
had  he  left  ? 

9.  A  man  had  8  rows  of  corn,  with  10  hills  in  a 
row.     The  cows  ate  50  hills.     How  many  were  left  ? 
Make  a  picture. 

10.  A  man  had  8  sheep  in  one  pen  and  6  in  another. 
Five  of  them  got  away.     How  many  were  left  ? 

11.  5  +  3-4  +  9  +  3^-5-4  +  9=? 

12.  5x7  +  7-2-? 

13.  Add,  subtract,  and  multiply  the  numbers  in  each 
of  these  .pairs : 

4,  7     5,  8     10,  6     17,  2     5,  9     11,  4     6,  6     9,  4 

14.  What  will  7  tables  cost  at  8  dollars  each? 

15.  How  many  days  in  8  school  weeks  ? 

16.  There  are  8  quarts  in  a  peck.     How  many  quarts 
in  7  pecks  ? 

17.  A  boy  gave  6  cents  for  an  orange,  8  cents  for 
pencils,  and  10  cents  for  a  ball.     How  many  cents  did 
he  pay  for  all  ? 

18.  Add  9?  7,  and  8,  and  then  subtract  5. 


42  PRIMARY   ARITHMETIC 

DIVISION 

28.  Children  watch.  Teacher  take  4  counters.  Lay  down 
two  counters,  and  two  more.  Thus,  II  II.  Children  do  the 
same. 

What  did  you  do  ? 

How  many  times  did  you  lay  down  two  counters  ? 

How  many  counters  did  you  take  ? 

Take  4  crayons.  Give  me  two  crayons.  Give  me 
two  more.  How  many  times  did  you  give  me  two 
crayons  ? 

How  many  2's  in  4  ? 

Take  6  sticks.  Lay  2  of  them.  Lay  2  more.  Lay 
2  more.  Thus,  II  II  II.  How  many  times  did  you  lay 
down  2  sticks  ? 

Make  6  marks.  Point  them  off  in  twos.  Thus,  II,  II,  II. 

How  many  groups  are  there  ? 

How  many  times  must  you  make  2  marks  to  have 
6  marks  ? 

How  many  27s  in  6  ? 

So  on  till  you  have  taught  "  there  are  ten  2's  in  20." 
Children  write  the  table  thus : 


2-*-2  =  l 

12-2=    6 

4-2  =  2 

14-2=    7 

6-2  =  3 

16-2=    8 

8-2  =  4 

18-2=    9 

10  -  2  =  5 

20  -  2  =  10 

PRIMARY   ARITHMETIC 


43 


How  many  pears  on  the  table  in  the  picture  ? 

To  how  many  children  can  the  girl  give  the  six  pears, 
if  she  gives  2  pears  to  each  child  ? 

To  how  many  sick  people  can  she  give  the  6  roses, 
if  she  gives  3  roses  to  each  ? 

1.  A  boy  has  4  cents.      How  many  pencils  can  he 
buy  at  2  cents  apiece  ? 

2.  A  boy  can  earn  2  cents  in  an  hour.    In  how  many 
hours  can  he  earn  10  cents?    14  cents?    18  cents?    6 
cents?    8  cents?    16  cents?    20  cents? 

3.  How  many  2's  in  10  ?   In  18  ?    In  12  ?   In  20  ? 

b 

BLACKBOARD   DRILL 

Divide  each  of  the  numbers  around 
the  circle  by  2.     Answer  quickly. 


44  PRIMARY   ARITHMETIC 

29.    Teacher  and  children  each  take  6  counters. 

Lay  3  of  them.     Lay  3  more.     Thus,  III  III. 
Children  tell  what  has  been  done. 

How  many  counters  in  each  group  ? 

How  many  groups  ? 

How  many  groups  of  three-counters  in  six  counters  ? 

How  many  groups  of  3-crayons  in  6  crayons  ? 

How  many  3-cents  in  6  cents  ? 


OO        CO 


00 


0  O  O        O  O  O 

How  many  apples  are  in  the  first  row  ?      How  manj 
in  the  second  row  ? 

Tell  two  ways  of  making  6. 
How  many  3's  in  6  ? 

Similarly  with  9,  12,  etc.,  counters. 
Children  write  the  table  thus : 


3 

-8-3  =  1 

18 

.      0   

6 

6 

Q         O 

T-    O    £ 

21 

-1-3.  a 

7 

9 

-3  =  3 

24 

.      O  

8 

12 

-3  =  4 

27 

-3  = 

9 

15 

-3  =  5 

30 

.      O    

10 

PRIMARY   ARITHMETIC 


45 


BLACKBOARD   DRILL 

1  5        Divide  each  of  the  numbers  around 
the  circle  by  3. 


1.  How  many  pencils  at  3  cents  each  will  12  cents 
buy? 

2.  How  many  suits  can  be  made  from  18  yards  of 
cloth  if  it  takes  3  yards  for  one  suit  ? 

3.  How  many  yards  in  30  feet  ? 

4.  Twenty-one  boys  stood  in  three  equal  lines  for  ex- 
ercises.    How  many  boys  were  in  each  line  ? 

5.  If  a  man  ploughs  3  acres  in  one  day,  in  how  many 
days  can  he  plough  24  acres  ? 

In  a  similar  manner,  teach  the  entire  table  of  division. 


30. 


TABLE  OF  DIVISION 


1-1=  1 

2-2=  1 

3-3=  1 

4-4=  1 

5-  5=  1 

2-1  =  2 

4-2=  2 

6-3=  2 

8-4=  2 

10-  5=  2 

3-1  =  3 

6-2=  3 

9-3=  3 

12-4=  3 

15-  5=  3 

4-1=  4 

8-r-2=  4 

12-3=  4 

16-4  =  4 

20-  5=  4 

5-1=  5 

10-2=  5 

15-3=  5 

20-4=  5 

25-i-  5=  5 

6-*-!  =  6 

12-2=  6 

18-3=  6 

24-4=  6 

30-  5=  6 

7-1  =  7 

14-2=  7 

21-3=  7 

28-4=  7 

35-f-  5=  7 

8-s-l=  8 

16-2=  8 

24-3=  8 

32-4=  8 

40-  5=  8 

9-5-1=  9 

18-2=  9 

27-3=  9 

36-4=  9 

45-j-  5=  9 

10-1  =  10 

20-2=10 

30-3  =  10 

40-4  =  10 

50-j-  5=10 

46 


PRIMARY   ARITHMETIC 


TABLE  OF  DIVISION  (Continued) 


6-6=  1 

7-7  =  1 

8-8=  1 

9-9=  1 

10-10=  1 

12-s-6=  2 

14-7=  2 

16-8=  2 

18-9=  2 

20-10=  2 

18-6=  3 

21-7=  3 

24-8=  3 

27-9=  3 

30-10=  3 

24-6=  4 

28-7=  4 

32-8=  4 

36-9=  4 

40-10  =  4 

30-6=  5 

35-7=  5 

40-8=  5 

45-9=  5 

50-10=  5 

36-6=  6 

42-7  =  6 

48-,-8=  6 

54-9=  6 

60-10=  6 

42-6=  7 

49-7=  7 

56-8=  7 

63-9=  7 

70-10  =  7 

48-6=  8 

56-7  =  8 

64-8  =  8 

72-9=  8 

80-10=  8 

54-6=  9 

63-7=  9 

72-8=  9 

81-9=  9 

90-10  =  9 

60-6=10 

70-7=10 

80-8=10 

90-^-9=10 

100-10=10 

1.  15-3  =  ? 

2.  15-5  =  ? 

3.  15  =  5  x  ? 

4.  15  =  3  x  ? 

5.  56  =  8  x  ? 

6.  56  =  7  x  ? 

7.  56^-7  =  ? 

8.  56-8  =  ? 

9.  54-9  =  ? 

10.  54-6  =  ? 

11.  54  =  9  x  ? 

12.  54  =  6  x  ? 

13.  40-4  =  ? 


14.  40-10=  ? 

15.  40  =  10  x  ? 

16.  40  =    4  x  ? 

17.  27  =    9  x  ? 

18.  27  =    3  x  ? 

19.  27-   3=  ? 

20.  27-    9=  ? 

21.  72-    9=  ? 

22.  72-    8=  ? 

23.  72  =?  x  8 

24.  72  =    9  x  ? 

25.  70  x    ?  =  70 


DIVISION  DRILL  CHART 

This  chart  contains  all  divisions  in  which  the  dividend  does 
not  exceed  100  and  the  divisor  and  quotient  do  not  exceed  10. 


PRIMARY   ARITHMETIC 


47 


It  should  be  used  daily  till  mastered.     Vary  the  work,  as  sug- 
gested with  the  previous  drill  charts.     Drill  persistently. 


10)100 

6)30 

9)90 

1)1 

6)18 

9)9 

1)4 

6)60 

6)54 

7)28 

7)42 

1)5 

6)24 

9)81 

3)9 

6)12 

5)15 

10)20 

4)24 

8)40 

2)18 

9)27 

6)36 

10)90 

2)14 

10)10 

4)20 

9)36 

2)2 

6)48 

7)35 

3)30 

8)56 

2)16 

9)18 

3)6 

9)72 

3)3 

10)60 

5)10 

1)6 

10)30 

5)40 
3)12 

6)6 

5)20 

8)48 

7)70 

7)21 

8)64 

2)4 

6)42 

7)28 

9)63 

1)2 

10)40 

3)15 

9)45 

3)18 

10)80 

7)49 

8)16 

1)10 

3)27 

7)63 

2)6 

8)24 

4)8 

7)14 

4)4 

11? 

4)16 

10)50 

2)12 

4)12 

9)54 

2)10 

5)45 

3)21 

8)32 

7)56 

8)8 

5)35 

5)25 

3)24 

8)72 

1)8 

10)70 

1)7 

5)5 

4)40 

4)36 

5)30 

II9 

8)80 

2)8 

5)50 

2)20 

4)32 

7)7 

31.  1.  Take  24  counters.  Divide  them  into  4  equal 
groups.  How  many  are  there  in  each  group  ?  How 
many  4's  are  there  in  24  ?  How  many  6?s  are  there 
in  24? 

2.  Take    15    counters.     Divide   them    into   3   equal 
parts.     How  many  are  there  in  each  part  ?     How  many 
3's  in  15  ?     How  many  5?s  in  15  ? 

3.  Two  pints  will  fill  a  quart  measure.     How  many 


48  PRIMARY   ARITHMETIC 

quart  measures  will  8  pints  fill?     12  pints?     6  pints? 
18  pints?     20  pints?     16  pints?     14  pints?     24  pints? 

4.  An  orchard  of  28  trees  has  7  trees  in  each  row. 
How  many  rows  are  there  ?     Make  a  picture  of  the 
orchard. 

5.  Make  a  picture  of  an  orchard  having  30  trees  with 
10  trees  in  each  row.     How  many  rows  are  there  ? 

6.  A  man  has  72  peaches  in  9  baskets,  the  same 
number  in  each  basket.     How  many  peaches  in  each 
basket  ? 

7.  If  a  man  puts  4  plums  in  a  row  in  a  basket, 
how  many  rows  would  hold  24  plums?     Make  a  pic- 
ture, thus, 


8.  Make  a  picture  of  48  birds  with  8  in  each  flock. 
How  many  flocks  ? 

9.  A  man  had  81  cents.     He  divided  them  among 
some  boys,  giving  each  boy  9  cents.     How  many  boys 
were  there  ? 

10.  A  man's  wages  are  18  dollars  per  week.     How. 
much  a  day  does  he  get  ? 

11.  Divide  63  sheep  into  7  equal  flocks.     How  many 
in  each  flock  ?     Make  a  picture. 

12.  If  you  can  buy  5  sheets  of  paper  for  a  cent,  how 
many  cents  will  pay  for  50  sheets  ? 


PRIMARY   ARITHMETIC 


BLACKBOARD  DRILL 


49 


oooooooo 

32.    How  many  apples  do  you  see  here  ? 
If  these  8  apples  are  divided  equally  between  two 
boys,  how  many  apples  will  each  boy  receive? 
How  many  apples  are  one  half  of  8  apples  ? 

1.  10  dollars  -*-  2  are  how  many  dollars  ? 

2.  i  of  10  dollars  are  how  many  dollars? 

3.  How  do  you  find  \  of  10  dollars  ? 

4.  8-^2  are  how  many  ? 

5.  l  of  8  are  how  many  ? 

6.  How  do  you  find  \  of  8  ? 

7.  16  quarts  divided  by  2  are  how  many  quarts? 

8.  \  of  16  quarts  are  how  many  quarts? 


50  PRIMARY  ARITHMETIC 

9.    How  do  you  find  ^  of  a  number  ? 

10.  Find  1  of  12.  12.    Find  1  of  18  cents. 

11.  Find  i  of  6  pencils.       13.   Find  1  of  4. 

ooooooooo 

14.  If  these  9  apples  are  divided  equally  among  3 
boys,  how  many  will  each  receive  ? 

15.  ^  of  9  apples  are  how  many  apples  ? 

16.  9  bushels  -*-  3  are  how  many  bushels? 

17.  ^  of  9  bushels  are  how  many  bushels  ? 

18.  How  do  you  find  J  of  a  number  ? 

19.  Find  l  of  21.  23.    Find  l  of  24. 

20.  Find  l  of  30.  24.    Find  £  of  27. 

21.  Find!  of  12.  25.   Find  1  of  15  days. 

22.  Find  i  of  6.  26.    Find  1  of. 3. 

33.    1.  8  quarts -5- 4  are  how  many  quarts? 

2.  1  of  8  quarts  are  how  many  quarts  ? 

3.  12  -i-  4  are  how  many  ? 

4.  ^  of  12  are  how  many  ? 

5.  20  cents  -s-  4  are  how  many  cents  ? 

6.  1  of  20  cents  are  how  many  cents  ? 

7.  ^  of  24  are  how  many  ? 

8.  How  do  you  find  l  of  a  number  ? 

9.  Find  J  of  16.  12.    Find  J  of  28  pounds. 

10.  Find  1  of  40  pounds.     13.    Find  |  of  36  pounds. 

11.  Find  l  of  32  apples.      14.    Find  J  of  4. 

15.  Divide  15  by  5. 

16.  |-  of  15  are  how  many  ? 


PRIMARY   ARITHMETIC  51 

17.  30  -s-  5  are  how  many  ? 

18.  Find  1  of  30  marbles. 

o 

19.  How  do  you  find  ^  of  a  number  ? 

20.  Find  £  of  40  feet. 

21.  Find  £  of  10  toes. 

22.  Find  £  of  35  houses. 

23.  Find  l  of  45. 

34.  1.    How  can  you  find  ^  of  a  number?     \  of  a 
number?     £?     £?     T^? 

2.  Find  l  of  40.  5.    Find  £  of  54. 

3.  Find  l  of  49.  6.   Find  ^  of  100. 

4.  Find  £  of  36.  7.    Find  £  of  45. 

8.  Hugh  has  20  rabbits  and  Ralph  has  1  as  many. 
How  many  has  Ralph  ? 

9.  Edna  has   4   dolls  and   Susan  has  \  as  many. 
How  many  dolls  has  Susan  ? 

10.  Mr.  Smith  walked  48  miles  and  Mr.  Fox  walked 
\  as  far.     How  many  miles  did  Mr.  Fox  walk  ? 

11.  William  had  40  marbles  and  Frank  had  ^  as 
many.     How  many  had  both  ? 

12.  There  were  50  men  in  a  factory.    |-  of  them  were 
black.     How  many  were  white  ? 

13.  Kate  solved  42  problems ;  Ruth  solved  \  as  many. 
How  many  did  Ruth  solve  ? 

35.  1.    How  many  twos  in  eight? 

2.  How  many  threes  in  ten,  and  how  many  over? 

3.  \  of  10  men  are  how  many  men  ? 


10.    3x3 

8-5 

4  +  4 

11.    8-6 

11-4 

3x2 

12.   5  +  3 

6  +  5 

5x2 

13.    7  +  2 

11-5 

6  +  4 

52  PRIMARY   ARITHMETIC 

4.  Two  mice  have  8  feet.     How  many  feet  has  one 
mouse  ? 

5.  If  4  oranges  cost  8  cents,  how  many  cents  does 
one  orange  cost  ? 

6.  If  3  balls  cost  9  cents,  what  is  the  cost  of  1  ball  ? 

7.  How  many  nickels  in  a  dime  ? 

8.  How  many  two-cent  pieces  in  ten  cents?     In  8 
cents  ? 

9.  2)10         4)8         3)9         5)10         2)8         3)6 

W-n-2 

lof  6 
iof  8 

14.    If  5  pencils  cost  10  cents,  what  does  one  pencil 
cost? 

15o    Put  8  sheep  in  4  pens.    How  many  sheep  in  each 
pen  ?     (Picture.) 

16.  How  many  two-cent  stamps   can   I  buy  for  8 
cents  ? 

17.  Make    problems    for    the    numbers    in   Ex.    10. 
Ex.  11.     Ex.  12. 

18.  Make  a  problem  for  -|  of  6. 

19.  Make  a  problem  for  J  of  8. 

36.    1.    Eight  boys  and  one  boy  are  how  many  boys? 

2.  One  ox  and  5  oxen  are  how  many  oxen  ? 

3.  If  1  sheep  costs  $  3,  what  will  3  sheep  cost  ? 

NOTE.  —  Teach  the  use  of  the  dollar  mark. 


PRIMARY   ARITHMETIC  53 

4.  How  many  knives   can  I  buy  for   $  10,  if   one 
knife  costs  $2? 

5.  If  4  geese  cost  $  8,  what  does  1  goose  cost  ? 


6. 

Add 

3 

5 

6 

5 

7 

3 

•5 

2 

3 

4 

5 

3 

0 

4 

7. 

Subtract 

8 

9 

10 

10 

9 

6 

8 

-3 

-5 

— 

6 

-10 

-6 

— 

3 

-2 

8. 

4x2 

8x 

1 

2 

X 

4 

lOx 

0 

2x3 

9. 

6x1 

3x 

3 

5 

X 

2 

10  x 

1 

8^4 

10. 

5)10 

4)8 

3' 

2 

)6 

2)10 

4)4 

2)8 

11.  Mary  has  two  dolls,  and  Annie  has  nine:     How 
many  have  both  ? 

12.  There  are  5  chairs  in  one  row  and  6  in  another. 
How  many  chairs  in  all  ? 

13.  John  had  10  balls  and  lost  three.     How  many 
had  he  left? 

14.  How  many  cents  are   2   cents,  3   cents,  and  5 
cents  ? 

15.  How  many  boys  are  2  boys,  4  boys,  and  5  boys? 

37.    1.    A  window  had  10  panes  of  glass  and  a  boy 
broke  3  panes.     How  many  were  left  ? 

2.  If  a  pail  holds  6  quarts,  and  there  are  5  quarts 
of  milk  in  it,  how  many  quarts  more  will  it  hold  ? 

3.  Four  teams  of  goats  are  how  many  goats  ? 

4.  How  many  pair  will  10  shoes  make? 


54  PRIMARY   ARITHMETIC 

5.  There  were  10  white  mice  in  a  box  and  7  ran 
out.     How  many  were  left  in  the  box  ? 

6.  What  3  pieces  of  money  make  5  cents  ? 

7.  How  many  three-cent  cakes  can  you  buy  for  10 
cents,  and  how  much  will  you  have  left  ? 

8.  If  a  six-quart  pail  is  half  full,  how  many  quarts 
are  in  the  pail  ? 

9.  How  much  less  than  a  dime  is  3  cents  ? 

10.  3   books   cost    $6.     What  will   one   book  cost? 
What  will  5  books  cost? 

11.  I  bought  an  orange  for  3  cents  and  candy  for 
5  cents.     How  much  money  did  I  spend  ? 

12.  I-  of  6  is  what  ?     £  of  8  is  what? 

13.  i  of  10  is  what  ?     \  of  10  is  what  ? 

14.  3x?=9.     9-3  =  ?     10-4  =  ?     6  +  3  =  ? 

15.  ?  +  4  =  8.     8-4  =  ?     9-?  =  4.     10-?  =  8. 

16.  How  do  you  find  \  of  a  number?     ^?     ^? 

38.  1.  Add  3  (2)  6  (3)  2  (4)  5  (5)  1  (6)  4  (7)  3 
433  2753 
3  1  •£  3_  2  1  3 

8.  5  +  3-1  =  ?     3  +  3-2  =  ?     2  +  2  +  2  =  ? 

9.  6-4  +  2  =  ?     8-4-2  =  ?     3  +  3  +  3  =  ? 

10.  \  of  10,     i  of  6,     3x3,     5x2. 

11.  \  of  8,       \  of  9,     4x2,     S-s-4. 

12.  Ned  lives  6  blocks  east  of  the  school,  and  Fred  4 
blocks  east.    How  far  from  Ned's  to  Fred's  ?    (Picture.) 


PRIMARY   ARITHMETIC  55 

13.  John  lives  4  blocks  west  of  the  school.     How 
far  from  John's   to    Ned's  ?     From  Ned's   to  John's  ? 
(Picture.) 

14.  One  week  and  5  days  are  how  many  days  ? 

15.  Nellie  had  5  two-cent  pieces.    She  bought  a  book 
for  4  cents,  and  a  pencil  for  3  cents.     How  much  money 
did  she  spend  ?     How  much  was  left  ? 

16.  May  had  ten  cents  and  spent  one-fifth  of  it  for  a 
pencil.     How  much  did  the  pencil  cost,  and  how  much 
has  she  left? 

17.  From  three  3's  take  two  4's. 

18.  One  book  costs   $4.     How  much  will  2  books 
cost? 

39.    1.    A  farmer  had  11  turkeys  and  sold  6  of  them. 
How  many  had  he  left  ? 

2.  If  there  are  two  nests,  with  5  eggs  in  each  nest, 
how  many  eggs  in  both  nests  ?     (Picture.) 

3.  If  George  had  10  cents  and  gave  ^  to  his  sister, 
how  much  will  she  have  ?      How  much  will  he  have 
left? 

4.  Rose  had  3  apples;    her  brother  had  twice   as 
many.     How  many  had  her  brother  ?     How  many  had 
both? 

5.  A  hen  had  11  chickens;    2  were  black,  4  were 
brown,  and  the   rest  were   white.      How  many  were 
white  ? 

6.  A  lady  bought  11  yards  of  cloth,  and  used  6 
yards.     How  many  has  she  left  ? 


56  PRIMARY   ARITHMETIC 

7.  May  is  11  years  old.     Maud  is  4  years  younger. 
How  old  is  Maud  ? 

8.  3  +  4  +  2     8-3-2     5x2  +  1 

9.  2  +  7  +  2     7  +  4-6     3x3  +  2 

10.  2  +  2  +  7     6  +  5-8     4  +  4  +  3 

11.  Add  3  (12)1  (13)2  (14)3  (15)  2  (16)  3  (17)4 

4  32  34  1  2 
2523333 
2252112 


40.    1.    One  tooth  and  11  teeth  are  how  many  teeth? 

2.  A  dime  and  a  two-cent  piece  make  how  much  ? 

3.  Six  two-cent  pieces  are  how  much  money? 

4.  How  many  cents  in  4  three-cent  pieces  ? 

5.  How  many  2-cent  stamps  can  you  buy  for  12 
cents  ? 

6.  In  12  pencils  how  many  dozen  ? 

7.  Find  the  cost  of  4  oranges  at  3  cents  apiece. 

8.  If  one  hat  costs  $  6,,  what  will  10  hats  cost  ? 

9.  Mary  has  9  cents,  Lillie  has  6  times  as  much. 
How  much  has  Lillie  ? 

10.  A  pint  of  milk  costs  2  cents.     How  many  pints 
will  12  cents  buy? 

11.  4  triangles  have  how  many  angles?     (Picture.) 

12.  Four  men  and  18  men  are  how  many  men  ? 

13.  Twelve  eggs  less  7  eggs  are  how  many  eggs  ? 

14.  Three  times  four  balls  are  how  many  balls  ? 

15.  Three  squares  have  how  many  sides  ?     (Picture.) 


PRIMARY   ARITHMETIC  57 

16.  Twelve  feet  less  one  foot  are  how  many  feet  ? 

17.  If  there  are  12  plants  in  four  rows,  how  many 
plants  in  each  row  ?     (Picture.) 

18.  Fred  had  12  marbles.     He  gave  3  to  Henry  and 
2  to  Tom.     How  many  had  Fred  left  ? 

19.  Six  boys  can  wear  how  many  shoes? 

41.    1.    7  boys  can  wear  how  many  shoes  ? 

2.  How  many  2-cent  pieces  in  14  cents  ? 

3.  If  one  dress  costs  $  7,  what  will  2  dresses  cost  ? 

4.  In  14  days  how  many  weeks  ? 

5.  From  14  cents  take  9  cents.     How  many  cents 
are  left  ? 

6.  If  you  can  buy  1  peach  for  2  cents,  what  will  7 
peaches  cost  ? 

7.  Mary  has  4  three-cent  pieces  and  a  2-cent  piece. 
How  much  money  has  she  ? 

8.  There  were  14  children  in  a  class;  9  were  girls. 
How  many  were  boys  ? 

9.  If  it  takes  7  yards  of  cloth  for  one  dress,  how 
many  dresses  can  be  made  from  14  yards  ? 

10.  Mrs.  Smith  had  $  14  and  spent  $  8  for  a  dress. 
How  many  dollars  were  left? 

11.  1x15  £of  15  15-    4 

12.  15-*- 15  lof  15  9+    6 

13.  15  x    1  13+   2  15-9 

14.  3x5  3  +  13  15-15 

15.  Make  problems  for  : 

3x5  iof!5  13  +  2 


58  PRIMARY    ARITHMETIC 

42.    1.    There  are  7  red  apples  and  10  green  ones  in 
a  basket.     How  many  apples  are  in  the  basket  ? 

2.  Frank  had   9   balls  and  bought  8  more.     How 
many  had  he  then  ? 

3.  Three  five-cent  pieces  and  a  two-cent  piece  are 
how  many  cents  ? 

4.  If  Henry  finds  9  eggs  in  one  nest  and  8  eggs  in 
another,  how  many  eggs  does  he  find  in  all  ?     (Picture.) 

5.  A  farmer  has   6   cows  in   one  yard  and   11   in 
another.     How  many  cows  in  both  yards  ?     (Picture.) 

6.  In  a  flock  of  17  sheep  6  sheep  are  black.     How 
many  are  white  ? 

7.  Frank  paid  17  cents  for  a  top  and  sold  it  for 
8  cents.     How  much  did  he  lose  ? 

8.  A  lady  bought  a  book  for  $17  and  paid   $9. 
How  much  did  she  still  owe  ? 

9.  16-    1  15+    1  lof  16 

10.  1x16  16-15  iof!6 

11.  16-f-   8  16-    1  lof  15 

12.  16  x    1  14+2  lof  15 

13.  4x4  16-14  11+   5 

14.  16-   4  2  +  14  10+   6 

15.  2x    8  13+3  16-9 

16.  16-2  13-13  16-0 

17.  8x2  12+   4  4  +  12 

18.  Count  to  16  by  2's;  by  4's. 

19.  Make  problems  for  16  -  4,  1  of  16,  16  *  8. 


PRIMARY   ARITHMETIC  59 

43.    1.    May  is  10  years  old ;  John  is  9  years  older. 
How  old  is  John  ? 

2.  May  had  6  cents,  Lucy  had  8  cents,  Ella  had 
5  cents.     How  much  had  they  all  ? 

3.  A  pole  was  19  feet  long.     I  cut  off  6  ft.  at  one 
time  and  10  ft.  at  another  time.     How  many  feet  were 
cut  off  and  how  many  were  left  ?     (Picture.) 

4.  From  nineteen  take  nine. 

5.  I  spent  $4  for  books,  $  10  for  a  case,  and  had 
$  5  left.     How  much  had  I  at  first  ? 

6.  19  children  were  at  school  and  7  of  them  went 
home.     How  many  are  left  ? 

7.  Jane  had  9  roses ;  her  sister  had  4  more.     How 
many  must  they  pick  to  have  19  roses  in  all? 


8. 

5+  ?  =  14 

?x6  = 

18 

|  of  18  =  ? 

9. 

16-8=    ? 

?-9  = 

6 

1  of  16  =  ? 

10. 

14-5=    ? 

12-  ?  = 

5 

1  of  18  =  ? 

11. 

7+  ?  =  13 

17-  ?  = 

8 

6  is  1  of  ? 

12. 

16  +  2=    ? 

?  +  2  = 

8 

4  is  i  of  ? 

13. 

5x4 

20-3 

lof  20 

14. 

20-e-5 

16  +  4 

fofl5 

15. 

Add     16      18 

17      15 

8 

452 

4        2 

3        5 

12 

14      12      13 

16.    5)20       4)20       2)16        9)18       3)15       4)12 

44.    1.    Take  3x4  from  2x9. 

2.    If  my  newspaper  comes  twice  a  week,  how  many 
papers  will  I  get  in  8  weeks  ? 


60  PRIMARY   ARITHMETIC 

3.  A  boy  had  18  apples.     He  gave  away  l  of  them 
and  lost  3.     How  many  had  he  left? 

4.  7  is  J  of  ?     12  is  twice  what  ? 

5.  4  is  J  of  ?     18  is  three  times  what  ? 

6.  A  hen  had  a  dozen  chickens.     Six  were  black 
and  the  rest  were  white.     How  many  were  white  ? 

7.  How  many  thumbs  have  four  pair  of  mittens  ? 

8.  Count  to  18  by  3'a. 

9.  A  ten-cent  piece  and  a  two-cent  piece  will  buy 
how  many  marbles  at  4  cents  each  ? 

10.  13  birds  were  on  a  tree  and  7  flew  away.     How 
many  remained  ? 

11.  Nellie  had  19  apples  and  gave  away  4  of  them 
and  ate  1.     How  many  had  she  left  ? 

12.  How  many  twos  in  20  ? 

13.  2x8-  ?  =  4  16.    i  of  20  =  5x? 

14.  18  =  3x5  +  ?  17.    7x2  +  3  =  ? 

15.  4x2x2=  ? 

45.  DRILL   EXERCISE 

1.  iof  20=  ?  3  x    4  =  ? 

z 

2.  i  of     ?  =  3  7  +  11  =  ? 

o 

3.  5x      3  +  2  =  ?  |of!8  =  ?' 

4.  iof  14=  ?  |ofl8  =  ? 

5.  iof     ?  =  8  19-     7  =  ? 

6.  20-   iof  14  =  ?  20*10  =  ? 


PRIMARY  ARITHMETIC  61 


7. 

Add  8     (8)  7     (9)  6     (10)  2     (11)  7     (12)  9 
3454            2            9 
5576            5            1 

4           4 

1862 

13. 

From  20  take  11, 

4,  6,  12,  9,  8. 

14. 

1  of  16  =  ?             t 

L  of  18  =  ?             1 

of  18  =  ? 

15. 

Iofl2  =  ?             j 

Lofl2  =  ?             1 

of  15  =  ? 

16. 

To  7  add  4,  12,  8, 

9,  3,  5. 

17. 

2)20          9)18 

2)16           3)15 

4)16 

18. 

Divide  50,  60,  70, 

80,  90  —  each  by 

10. 

19. 

5  in  15,  20,  10,  5, 

0. 

20. 

20-    1 

19+   1 

16+4 

21. 

1x20 

20-    1 

20-16 

22. 

20-20 

1  +  19 

4  +  16 

23. 

20  x    1 

20-19 

20-4 

24. 

2x10 

18+   2 

15+   5 

25. 

20-   2 

20-18 

20-15 

26. 

29-10 

20-2 

5  +  15 

46.    1.     Find  the  cost  of  8  pair  of  shoes  at  $3  a  pair. 

2.  If  a  man  earns  $12  a  week,  how  much  can  he 
earn  in  2  weeks  ? 

3.  How  many  eggs  in  2  dozen? 

4.  How  many  two-quart  pitchers  will  24  quarts  of 
water  fill  ? 

5.  How  many  threes  in  2  dozen  ? 


62 


PRIMARY  ARITHMETIC 


6.  What  number  is  J  of  24  ? 

7.  Find  the  cost  of  6  books  at  $4  each. 

8.  A  lady  bought  a  dozen  eggs,     l  of  them  were 
bad.     How  many  were  good  ? 

9.  My  square  table  is  6  feet  on  a  side.     How  many 
feet  of  fringe  will  it  take  to  go  around  it  ?     (Picture.) 

10.  Bought  6  lemons  for  24  cents.     What  did  one 
lemon  cost  ? 

11.  Two  weeks  and  10  days  are  how  many  days? 

12.  How  many  feet  have  3  cats  and  3  rats  ? 

13.  What  four  numbers  added  together  make  21  ? 

14.  iof!2ct.  =  ?       lof  $12  =  ?       ^of  18  =  ? 
15.^7)21        6)18        3)15        4)16     '  3)21        8)16 


16. 

8 

7 

62487 

9        8 

x2 

x3 

x3     x9     x4     +5     x3 

+  7     +6 

17. 

17 

18 

14         17         15 

7           9 

-6 

-9 

-2         -6         -2 

x3       +4 

18. 

i<* 

20  =  ? 

lof  15  =  ? 

lof  15  =  ? 

19. 

i  of 

18  =  ? 

lof  20  =  ? 

lof  21  =  ? 

20.  What  three  equal  numbers  in  21  ? 

21.  What  seven  equal  numbers  in  21  ? 


47.   1.   5x5  =  ? 

2.  25  +  5  = 

3.  of25 


Add  4,  5,  3,  5,  5. 
6+4+5+6+1=? 


99  TM* 

UNIVERSITY 


PRIMARY 
5  6 

5.  18  +  ?  =  25  3x8  =  ?     5x3  =  ? 

6.  25^-5  =  ?  24-^8  =  ? 

7.  Harry  bought  a  knife  for  15  cents  and  sold  it  for 
25  cents.     What  did  he  gain? 

8.  There  are  25  apples  in  a  basket.     I  take  |  of 
them.     How  many  do  I  take  ?     How*  many  are  left  ? 

9.  How  many  3-cent  pieces  in  27  cents  ? 

10.  How  many  nickels  in  a  quarter  ? 

11.  How  many  cents  in-nine  nickels? 

12.  Give  3  cents  to   each  of  nine  children.      How 
much  do  all  get  ? 

13.  John  bought  3  dozen  buttons  at  9  cents  a  dozen. 
How  much  did  they  cost  ? 

14.  If  9  books  cost  $27,  what  does  one  book  cost? 

15.  How  many  9's  in  27  ? 

16.  There  are  3  feet  in  a  yard.     How  many  yards  in 
27  feet  ?     (Picture.) 

48.     1.   A  table  has  four  sides;  each  side  is  7  feet 
long.     How  many  feet  around  the  table  ?     (Picture.) 

2.  7  oranges  cost  28  cents.     What  is  the  cost  of 
one  orange  ? 

3.  What  will  4  books  cost  at  7  cents  each  ? 

4.  7  pair  of  oxen  have  how  many  horns  ? 

5.  If  there  are  4  trees  in  a  row,  how  many  trees  in 
7  rows  ?     (Picture.) 

6.  What  three  equal  numbers  make  twenty-four? 


64  PRIMARY  ARITHMETIC 

7.  What  month,  has  28  days  ?     When  does  it  have 
29  days  ? 

8.  If  I  make  $  4  in  selling  a  stove,  how  many  stoves 
must  I  sell  to  make  $  28  ? 

9.  How  many  school  days  in  6  weeks  ? 

10.  Into    what    three    equal    numbers    can    30    be 
divided  ? 

11.  A  milkman  had  five  six-quart  cans  of  milk.    How 
much  milk  had  he  ? 

12.  How  many  5's  in  3  x  10  ? 

13.  $10  is  ^  of  how  much  money  ? 

14.  How  many  two-cent   stamps  can  I  buy  for  30 
cents  ? 

15.  What  piece  of  money  is  l  of  30  cents  ? 

16.  John  has  30  cents,  and  Mary  has  |-  as  much. 
How  much  has  Mary? 

17.  If  8  pencils  cost  32  cents,  what  does  1  pencil 
cost  ?     What  will  7  pencils  cost  ? 

18.  If  32  cents  are  divided  equally  among  8  chil- 
dren, how  many  cents  will  each  receive  ? 

19.  What  will  8  pounds  of  rice  cost  at  4  cents  a 
pound  ? 

• 

49.    1.    How  many  8's  in  35,  and  how  many  over? 

2.  In  36  feet  how  many  yards  ?     (Picture.) 

3.  How  many   boys   will    it   take   for   4    baseball 
nines  ?     (Picture  ball  ground.) 

4.  How  many  months  in  3  years  ? 

5.  What  cost  9  lemons  at  36  cents  a  dozen? 


PRIMARY   ARITHMETIC  65 

6.  A  man  earns  $9  a  week.     How  much  does  he 
earn  in  4  weeks  ? 

7.  How  many  4-dollar  chairs  can  be  bought  for  $  36  ? 

8.  How  many  eggs  in  3  dozen  ? 

9.  Three  boys  earned  36  cents.    How  much  was  that 
for  each  one  ? 

10.  What  two  equal  pieces  of  money  make  -£  of  36 
cents  ? 

11.  5x    7  =  ?  £of  35  7x    ?  =  35 

12.  35-   5  =  ?            |  of  28  6x    ?  =  30 

13.  35-*-   7  =  ?            J-of24  8+   ?  =  30 

14.  4  +  6  +  9  +  6  +  3  =  ?          17.  6  +  8  +  9  +  7  +  5  =  ? 

15.  7  +  4  +  3  +  7  +  2  =  ?          18.  2  +  7  +  6  +  4  +  6  =  ? 

16.  9  +  3  +  6  +  2  +  9  =  ?          19.  7  +  7  +  7  +  7  +  7  =  ? 

20.  Make  seven  rows  of  squares  with  five  squares  in 
a  row.     How  many  squares  ?  How  many  angles  have 
^  of  these  squares  ? 

21.  lofl6          Jof39  16 -s-    8 

22.  Jof32          Jof40  14-s-   2 

23.  iof27          Iof36  28-14         38-18 

24.  iof32        T1oof40  36-18 

25.  |  of  21          |  of  25  27^-   9         36-20 

50.    1.    In  16  dimes  how  many  cents,  and  how  many 
over? 

2.  A  father  gave  to  one  of  his  sons  30  cents,  to 
another  14  cents,  and  to  his  daughter  2  cents.  How 
much  did  he  give  them  in  all  ? 


66  PRIMARY   ARITHMETIC 

3.  I  bought  a  stove  for  $  40  and  a  table  for  1  as 
much.  How  much  did  both  cost  ? 

4.  Count  from  3  to  45  and  back  by  sixes. 

5.  Find  the  sum  of  7  times  4  and  4  times  2. 

6.  Add  3      (7)  9      (8)  9      (9)  6    (10)  4    (11)  6 


5 

4 

8 

11 

6 

5 

10 

6 

7 

9 

9 

11 

11 

3 

6 

3 

6 

5 

5 

2 

5 

8 

4 

9 

7 

1 

4 

7 

5 

9 

12.  Multiply  578694756 

9647387    10      6 

13.  36  is  how  many  times  6  ? 

14.  45  is  9  times  what  number  ? 

15.  45-9  +  3  =  ? 

16.  45-15  +  10  =  ?    49-7  =  ? 

17.  £of45     5x8  20.    *  of  42 

18.  i  of  45     7  x  6  21.   1  of  48 

19.  .Jof44 

51.    1.    How  many  cents  in  6  dimes  ? 

2.  How  many  school  days  in  8  weeks  ? 

3.  How  many  working  days  in  5  weeks  ? 

4.  In  48  eggs  how  many  dozen  ? 

5.  A  lady  bought  a  shawl  for  $30  and  a  dress  for 
as  much.     What  did  both  cost  ? 


PRIMARY  ARITHMETIC  67 

6.  If  I  buy  some  cloth  for  $44  and  sell  it  at  a  loss 
of  $13,  what  do  I  get  for  it  ? 

7.  If  a  pound  of  candy  costs  12  cents,  what  will 
4  pounds  cost  ? 

8.  How  many  nickels  in  $  .45  ? 

NOTE.  —  Teach  how  to  indicate  cents  by  means  of  the  decimal 
point  and  dollar  sign. 

9.  If  4   quarts  of  vinegar  can  be  bought  for  28 
cents,  how  many  quarts  can  be  bought  for  49  cents  ? 

10.  Mr.   Smith  gave   $50   to  his  five  boys.     How 
much  did  each  get  ? 

11.  lof  $.40  3x$.09 

12.  i-of$.42  4x$.ll 

13.  i  of  $  .49  8  x  $  .06 

14.  1  of  $  .48  4  x  $  .12 

15.  £of$.45 

16.  1  of  $.48  5x$.ll  4x8  +  6 

17.  45-  ?  =  9  ?x    6  =  48 

18.  49-f-7=?  ?  +  15  =  45 

19.  From  9x5  take  7x6. 

20.  How  many  days  does  a  man  work  in  nine  weeks  ? 

21.  A  load  of  potatoes  had  54  bushels.     I  bought  ^ 
of  the  load.     How  many  bushels  have  I  ? 

22.  How  many  hats  can  a  man  buy  for  $54  if  4  hats 
cost  $  24  ? 

52.    1.    If  8  bars  of  soap  cost  $.56,  what  is  the  cost 
of  one  bar  ? 


68  PRIMARY  ARITHMETIC 

2.  What  is  the  cost  of  9  Ib.  of  sugar  at  6  ct.  a 
pound  ? 

3.  Willie  has  20  marbles,  James  20,  and  John  10. 
How  many  have  all  ? 

4.  May  had  $.59.     She  spent  10  cents  for  paper. 
How  much  had  she  left  ? 

5.  Into  how  many  lots  of  7  acres  each  can  a  56-acre 
lot  be  divided  ? 

6.  How  many  days  in  6  weeks  ? 

7.  How  many  eggs  in  4  dozen  ? 

8.  If  I  owe  $.58  and  pay  all  but  10  cents,  how 
much  have  I  paid  ? 

9.  Max  bought  a  knife  for  41  cents  and  sold  it  so 
as  to  gain  10  cents.     What  did  he  sell  it  for  ? 

10. 


11. 


10  +  1 

10  +  2 

10  +  3 

10  +  4 

20  +  1 

20  +  2 

20  +  3 

20  +  4 

30  +  1 

30  +  2 

30  +  3 

30  +  4 

40  +  1 

40  +  2 

40  +  3 

40  +  4 

50  +  1 

50  +  2 

50  +  3 

50  +  4' 

10-2 

10-3 

10-4 

HMtf 

20-2 

20-3 

20-4 

20-5 

30-2 

30-3 

30-4 

•  30  T.  5 

40-2 

40-3 

40-4 

40-5 

50-2 

50-3 

50-4 

50-5 

12.    Count  to  55  by  fives. 

53.    1.    In  a  garden  are  48  plants  in  6  equal  rows. 
How  many  plants  in  each  row? 


PRIMARY  ARITHMETIC  69 


2.  How  many  weeks  must  a  man  work  to  earn 
if  he  earns  $  12  a  week  ? 

3.  A  boy  paid  $  .40  for  a  knife  and  $  .15  for  a  slate. 
What  was  the  cost  of  both  ? 

4.  From  a  piece  of  calico  containing  58  yards  I  cut 
18  yards.     How  many  yards  were  left  ? 

5.  If  I  earn  $  .09  a  day  for  a  week,  how  much  have 
I  earned  ? 

6.  At  8  cents  each,  what  will  7  cocoanuts  cost? 

7.  John  lives   10  blocks   east  of   the   school,  and 
William  15  blocks  west.     How  far  does  John  live  from 
William  ?     (Illustrate.) 

8.  If  a  ship  sails  63  miles  in  9  hours,  how  far  will 
she  sail  in  1  hour? 


9. 

11- 

K4 

11 

-4 

12 

-5 

12  H 

h5 

10. 

21- 

h4 

21 

-4 

22 

-5 

22  H 

h5 

11. 

31- 

\-4: 

31 

-4 

32 

-5 

32  H 

h5 

12. 
-"13. 

41- 
51- 

1-4 
h4 

41 
51 

-4 
-4 

42 
52 

-5 

-5 

42  H 
52  H 

h5 
-5 

/i4.  Count  to  60  by  5's ;  by  3's  ;  by  2's. 

15.  9x5      8x4       7x5      9x7 

]£.  9x4      8x6       6x7      7x7 

17.  9x6       8x5      7x8      6x6 

18.  9x3      8x8      7x4      11  x  4 

54.  1.    How  many  dimes  in  60  cents  ? 

2.  Bought   9   lamps  at  4  dollars   apiece,  and   sold 
them  at  7  dollars  apiece.     How  much  did  I  gain  ? 


70  PRIMARY   ARITHMETIC 

3.  What  cost  2  oranges  at  60  cents  a  dozen  ? 

4.  In  one  field   there   were  20   cows ;    in  another 
twice  as  many.     How  many  in  the  second  field  ?     How 
many  in  both  fields  ? 

5.  If  4  apples  cost  12  cents,  how  much  will  9  apples 
cost? 

6.  What  7  equal  numbers  make  56  ? 

7.  If  8  bars  of  soap  cost   $.56,  what  is  the  cost 
of  one  bar? 

&.  What  is  the  cost  of  9  pounds  of  sugar. at  6  cents 
a  pound  ? 

9.  Willie  has  20  marbles,  James  20,  and  John  10. 
How  many  have  all  ? 


16. 

13 

+  5 

13- 

6 

14 

+ 

7 

14- 

-7 

li. 

23 

+  5 

23- 

6 

24 

+ 

7 

24- 

-7 

12. 

33 

+  5 

33- 

6 

34 

+ 

7 

34- 

-7 

13. 

43 

+  5 

43- 

6 

44 

+ 

7 

44- 

-7 

14. 

53 

+  5 

53- 

6 

54 

+ 

7 

54- 

-7 

15. 

Add  6, 

9,  8,  7,  3,  4 

,  2,  15,  4. 

16. 

Add  8 

(17)  6 

(18) 

12 

(19) 

10 

(20) 

4 

12 

8 

2 

5 

6 

10 

4 

8 

4 

10 

8 

9 

11 

6 

» 

5 

9 

12 

9 

1 

5 

55.    1.    How  many  spools  of  thread  at  4  cents  a  spool 
can  you  buy  for  36  cents  ? 

2.    In  an  orchard  are  8  rows  of  trees  with  9  trees  in 
each  row.     How  many  trees  in  the  orchard  ? 


PRIMARY   ARITHMETIC  71 

3.  I  have  five  10-pound  jars  of  butter,  and  sell  it 
all  at  a  profit  of  6  cents  a  pound.     What  do  I  make  ? 

4.  How  many  pounds  of  steak  at  8  cents  a  pound 
can  I  buy  for  32  cents  ? 

5!    If  60  cents  be  paid  for  thread  at  4  cents  a  spool, 
how  many  spools  are  bought  ? 

6.  Count  from  6  to  61  and  back  by  fives. 

7.  Count  from  8  to  62  and  back  by  6's. 

§.    How  many  suits  of  clothes  can  be  made  from  63 
yards  of  cloth,  if  one  suit  takes  7  yards  ? 

9,    A  wagon  cost  $  64,  a  harness  ^  as  much.     What 
did  both  cost  ? 

1ft.    At  $  12  a  week,  how  much  will  a  man  earn  in  5 
weeks  ? 

11*    If  a  pair  of  boots  cost  $  6,  what  will  be  the  cost 
of  5  pair  ?    7  pair  ?    9  pair  ? 

12.    If  a  boy  can  ride  a  bicycle  6  miles  in  6  hours, 
how  far  can  he  go  in  an  hour  ? 

18.    At  7  cents  a  pound,  how  many  pounds  of  sugar 
can  I  buy  for  63  cents  ? 

14.  Count  from  5  to  69  and  back  by  fours. 

15.  Count  from  28  to  72  and  back  by  4's. 

16.  9  times  .4;  6  ;  3 ;  2 ;  9  ;  8 ;  7;  10 ;  11  ;  12. 
IT^Count  by  nines  to  108. 


i»r^J  +  7 

11-7 

12  +  7 

12-7 

le.  21  +  7 

21-7 

22  +  7 

22-7 

£0.   31  +  7 
21.   41  +  7 

31-7 
41-7 

32  +  7 
42  +  7 

32-7 

42-7 

72  PRIMARY   ARITHMETIC 

56.    1:     How  many  5-cent  pieces  in  50  cents? 
2.    How  many  eggs  in  6  dozen  ? 
3>.    What  must  I  pay  for  7  pencils  at  4  cents  each? 

4.  If  3  girls  can  do  a  piece  of  work  in  6  days,  in 
how  many  days  can  one  girl  do  it  ? 

5.  If  5  cents  is  J  of  my  money,  how  much  money 
have  I  ? 

6.  How  many  months  in  6  years  ? 

7.  How  many  boots  in  1  dozen  pair  ? 

8.  How  many  are  6  dozen  oranges  less  8  oranges  ? 

9.  What  four  pieces  of  money  make  75  cents  ? 

10.  In  72  books  how  many  dozen  ?  • 

11.  If  it  takes  9  yards  of  calico  for  one  dress,  what 
will  it  take  for  8  dresses  ? 


12".   9x    8 

12x6 

63+   7 

70-40 

13.   4x5 

72  +  9 

15  +  15 

75  -,25 

14.    3x12 

64  +  8 

12  +  20 

36-20 

15.   8x    8 

7x9 

18  +  10 

50-25 

16-.    Count  from  7  to  73  and  back  by  sixes. 
17.    Count  from  8  to  78  and  back  by  sevens. 


18. 

11  +  9  ' 

11 

-9 

13 

+  8 

13 

-8 

i 

19. 

21  H 

h9 

21 

-9 

23 

+  8 

23 

-8 

20. 

31  H 

h9 

31 

-9 

33 

+  8 

33 

-8 

2J-. 

41  H 

h9 

41 

-9 

43 

+  8 

43 

-8 

22. 

51- 

h9 

51 

-9 

53 

+  8 

53 

-8 

l 

23. 

i 

61- 

h9 

61 

-9 

63 

+  8 

63 

-8 

PRIMARY  ARITHMETIC  73 

57.    1.    How  many  dimes  in  70  cents? 

2.  Twenty-eight   horseshoes   will    shoe  how  many 

horses  ? 

i 

3.  In  our  class  there  are  seven  children  in  each 
row.     How  many  children  in  8  rows  ? 

4.  Will  had   35  papers,  and  Harry  had  twice  as 
many.     How  many  had  Harry  ? 

5.  At  4  dollars  a  day,  how  much  does  a  man. .earn 
in  2  weeks  ? 

d.    If  I  have   $  8  in  quarters,  how  many  quarters 
have  I ?  * 

fit  7.    How  many  legs  have  a  dozen  flies  ? 

$.    At  7  cents  each,  how  many  tablets  can  I  buy  for 
84  cents? 

9.    John  had  eighty-four  apples.    How  many  dozen 
did  he  have  ? 

10.    If  1  dozen  oranges  cost  48  cents,  what  does  1 
orange  cost? 

1}.  12  +  8  +  6+9  +  4  +  5  +  3  +  2-? 
12.  8  +  9  +  10  +  6  +  5  +  6+4  +  3  =  ? 
1^.  3x3x3x3  =  ?  2x2x2x2x2x2  =  ? 


14. 

2H 

h9 

52 

+  9 

52 

-9 

6H 

-5 

1£. 

12  H 

h9 

62 

+  9 

42 

-9 

16  H 

-5 

I 

l§. 

22- 

h9 

72 

+  9 

'   32 

-9 

26  H 

^5 

iV. 

32- 

h9 

72 

-9 

22 

_  9 

36  H 

-5' 

18. 

42- 

(-9 

62 

-9 

12 

-9 

46  H 

(-5 

74  PRIMARY   ARITHMETIC 

58.    1.    How  many  school  weeks  in  40  days? 

2.  How  much  sugar  at  $  .08  a  pound  can  I  buy  for 
$.72? 

3.  Emma  is  9  years  old  ;  her  father  is  five  times  as 
old.     What  is  her  father's  age  ? 

4.  If  you  earn  12  cents  in  a  week,  how  much  do 
you  earn  in  a  month  ? 

5.  How  many  quarts  of  oil  do  we  use  in  12  weeks 
if  we  use  1  quart  each  day  ? 

6.  There  are  7  days  in  a  week.     How  many  days 
in  3  weeks  and  5  days  ? 

7.  Ned  has  J  of  27  cents.     George  has  ^  of  28  cents. 
How  many  cents  have  both  ? 

8.  Eight  chairs  cost   $32.     How  much  apiece   do 
they  cost  ? 

9.  There  are  12  things  in  a  dozen.     4x9  are  how 
many  dozen  ? 

10.  Seven  apples  cut  into  quarters  make  how  many 
quarters  ? 

11.  A  lady  had  32  apples.     She  gave  5  boys  6  apples 
apiece.     How  many  had  she  left  ? 


12. 

72 

+ 

6+1 

'  =  20 

100  + 

10- 

?=  1 

13. 

7 

X 

9 

100- 

4 

19  + 

8 

19- 

8 

14. 

100 

X 

5 

96  + 

12 

29  + 

8 

29- 

8 

15. 

18 

X 

4 

72  + 

12 

39  + 

8 

39- 

8 

16. 

16 

X 

5 

88  + 

11 

49  + 

8 

49- 

8 

17. 

14 

X 

5 

72  + 

9 

59  + 

8 

59- 

8 

2 

CQ 


Pu 

£ 


•s, 


PART    SECOND 

NOTATION  AND   NUMERATION 

1.  That  which  tells  how  many  is  Number.      As,  11,  12 
books,  15  cents. 

2.  One  is  a  Unit.     As,  1,  1  dollar,  1  horse. 

3.  Every  number  is  made  up  of  units.     Three  contains  3 
units.     Twenty  contains  20  units.     Fifty  trees  contains  50 
units. 

4.  Writing  numbers  is  Notation.     As,  7,  VII,  seven. 

5.  Writing  numbers  in  figures  is  Arabic  Notation.     As,  13. 

6.  In  Arabic  notation,  ten  figures  are  used  in  writing  num- 
bers.     They  are  0,  1,  2,  3,  4,  5,  6,  7,  8,  9.      They  are  called 
naught,  one,  two,  three,  four,  five,  six,  seven,  eight,  nine. 
The  first  figure  is  also  sometimes  called  a  cipher  or  zero. 

One  is  written 1 

Ten  is  written 10 

One  hundred  is  written 100 

One  thousand  is  written •        1000 

Ten  thousand  is  written 10000 

One  hundred  thousand  is  written     .     .     .  100000 

One  million  is  written 1000000 

Ten  million  is  written 10000000 

One  hundred  million  is  written  ....  100000000 

7.  Read  the  above  numbers.     What  would  the  numbers 
be  if  5  were  used  where  1  is  ? 

If  7  were  used  where  1  is  ?         If  3  were  used  where  1  is  ? 

75 


76  PRIMARY   ARITHMETIC 

How  many  ones  are  there  in  10  ? 

How  many  tens  are  there  in  100  ? 

How  many  hundreds  are  there  in  1000  ? 

How  many  thousands  are  there  in  10,000  ? 

How  many  ten-thousands  are  there  in  100,000  ? 

How  many  hundred-thousands  are  there  in  1,000,000  ? 

How  many  millions  are  there  in  10,000,000  ? 

How  many  ten-millions  are  there  in  100,000,000? 

What  is  the  value  of  0  ? 

Since  0  has  no  value,  what  is  it  that  has  value  in  these 
numbers  ? 

How  does  the  value  of  the  figure  1  in  the  second  number 
compare  with  the  value  of  the  figure  1  in  the  first  number  ? 

The  1  in  the  third  number  with  the  1  in  the  second  num- 
ber ? 

The  1  in  the  fourth  number  with  the  1  in  the  third  number? 

The  1  in  any  of  these  numbers  with  the  1  in  the  number 
before  it  ? 

The  place  of  the  1  in  any  of  these  numbers  compares  how 
with  the  place  of  the  1  in  the  number  before  it  ?  Answer 
all  these  questions  about  the  numbers,  using  2,  3,  5,  or  7  in 
place  of  1. 

What  must  you  do  with  the  1,  2,  3,  5,  or  7  in  any  of  these 
numbers  to  get  the  number  after  it  ?  That  would  affect  the 
value  of  the  figure  how  ? 

What  would  you  have  to  do  with  the  1,  2,  3,  5,  or  7  in 
any  of  these  numbers  to  get  the  number  before  it  ?  How 
would  that  affect  the  value  of  the  figure  ? 

On  what,  then,  does  the  value  of  a  figure  depend  ? 

For  what  are  the  ciphers  used  ? 

8.  The  answers  to  the  foregoing  questions  show  the  fol- 
lowing : 


NOTATION   AND   NUMERATION 


77 


Principles  of  Arabic  Notation 

1.  Each  removal  of  a  figure  one  place  to  the  left 
increases  its  value  tenfold. 

2.  Each  removal  of  a  figure  one  place  to  the  right 
decreases  its  value  tenfold. 

3.  The  value  of  a  figure  depends  upon  its  place  in 
the  number. 

4.  Ciphers  are  used  to  give  the  other  figures  their 
proper  places. 


1OO,OOO,OOO  =  ONE  HUNDRED  MILLION 

.  10,OOO,OOO  =  TEN  MILLION  =  111     MILLION 

.     .  1,OOO,OOO  =  ONE  MILLION 
.     .    .     10O,OOO  =  ONE  HUNDRED  THOUSAND 
....     1O,OOO  =  TEN  THOUSAND  =  ±±±    THOUSAND 

1,000  =  ONE  THOUSAND 

100  =  ONE  HUNDRED 

10  =  TEN  =  HI     (UNITS) 

1  =  ONE 

111,111,111  =  111     MILLION,     HI    THOUSAND,     HI 


o 

m  z 
D 


3g5 


78  PRIMARY   ARITHMETIC 


Q 


§  Q  °  § 

E  o  £ 

UJ  CC  CC  Q.  Q 

£  a  »       g 


j       u       x 

i      i      1      I 

h  2  Z  j- 


O 

51    UJ 

UJ 
0 

5 

PLACE 

< 

51  u 

w  q 

DRED-TRILLIONS' 
TRILLIONS'  PLAC 

.LIONS'  PLACE 

DRED-BILLIONS'  1 

BILLIONS'  PLACE 

IONS'  PLACE 

DRED-MILLIONS' 

MILLIONS'  PLACE 

UJ 

0 

2 

CO 

z 

0 

DRED-THOUSAND 
THOUSANDS'  PL/! 

USANDS'  PLACE 

DREDS'  PLACE 

§5 

5l  ?• 

z  ± 

_i 

z 

Z 

_i 

Z 

Z 

_j 

Z    Z 

0 

Z 

2    t 

D    UJ 

E 

D 

UJ 

D    Id 

I 

D 

I    h 

h 

I 

h 

CO 

I 

h 

!E 

I    h 

h 

I 

h    3 

695,432,741,897,654  =  six  hundred  ninety-five 
trillion,  four  hundred  thirty-two  billion,  seven  hundred 
forty-one  million,  eight  hundred  ninety-seven  thousand, 
six  hundred  fifty-four. 

320,105  =  three  hundred  twenty  thousand,  one  hundred 
five. 

907,035,700  =  nine  hundred  seven  million,  thirty-five 
thousand,  seven  hundred. 

5,001,006  =  five  million,  one  thousand,  six. 

70,000,025  =  seventy  million,  twenty-five. 

13,000,000,500,000  =  thirteen  trillion,  five  hundred  thou- 
sand. 

11.  1.  Each  figure  occupies  a  place.  How  many  places 
are  there  in  a  period  ? 

2.  Beginning  at  the  right,  name  in  order  five  periods. 

3.  How  many  figures  are  there  in  five  periods  ? 

4.  How  many  places  are  there  in  five  periods  ? 

5.  Name  fifteen  places  in  order,  beginning  at  the  right. 


NUMERATION  79 

6.  In  reading  numbers,  when  you  come  to  a  period  com- 
posed of  three  ciphers,  what  do  you  read  for  that  period  ? 

7.  Why  is  it  necessary  to  use  three  ciphers  in  writing 
the  number  ? 

8.  How  does  the  name  of  each  period  compare  with  the 
name  of  its  right-hand  place  ? 

9.  Write  a  number  containing  one  period. 

10.  Write  a  number  containing  three  periods. 

11.  Write  a  number  containing  12  places.       How  many 
periods  are  there  in  such  a  number  ? 

NUMERATION 

12.  Naming  the  places  of  figures  and  reading  numbers  is 
Numeration.     Thus,  to  numerate  43,008,160,  you  should  say, 
"  Units,  tens,  hundreds,  thousands,  ten-thousands,  hundred- 
thousands,  millions,  ten-millions  —  forty-three  million,  eight 
thousand,  one  hundred  sixty." 

13.  Numerate  the  numbers  below  : 

1.  385  6.        35,000,730 

2.  1,421  7.  8,460,000 

3.  25,678  8.   423,000,501 

4.  315,129  9.  8,003,040,631 

5.  6,785,342  10.     8,900,760 

i 

14.  Write  in  figures  : 

1.  Two  hundred  thousand,  sixteen. 

2.  Eleven  thousand,  two. 

3.  Four  million,  six  hundred  eight  thousand,  three  hun- 
dred seventy-five. 


80  PRIMARY   ARITHMETIC 

4.  Twenty-five  thousand,  three  hundred  eighty-seven. 

5.  Nineteen  thousand,  seventeen. 

6.  Twenty-seven  million,  six  hundred  fifty-two. 

7.  Eighty  million,  six  hundred  nine  thousand,  four  hun- 
dred twenty -eight. 

8.  Four  hundred  thirty -six  thousand,  forty-one. 

9.  Six  hundred  twenty  million,  seventeen  thousand,  four 
hundred  seventy-seven. 

10.  One  hundred  fifty-seven   million,  six  hundred  eight 
thousand,  four  hundred  seventy-seven. 

11.  Three  billion,  fifty-seven  million,  four  hundred  seven- 
teen thousand  sixty. 

ROMAN   NOTATION 

15.  The  Roman  notation,  instead  of  using  figures  to 
represent  numbers,  uses  seven  capital  letters,  as  follows  : 
I,  V,  X,  L,  C,  D,  M. 

Repeat  the  letters  in  the  above  order  until  you  can  say 
them  very  rapidly. 

The  values  of  these  letters  are  as  follows : 

1=  i  (ii  =  2,  111  =  3). 

V  =  5  (IV  =  4,  VI  =  6,  VII  =  7,  VIII  =  8). 

X  =  10  (IX  =  9,  XI  =  11,  XII  =  12,  XXX  =  30). 

L  =  50  (XL  =  40,  LX  =  60,  LXXXVIII  =  88). 

C  =  100  (XC  =  90,  CCC  =  300,  XCIX  =  99). 

D  =  500  (CD  =  400,  DCCIX  =  709). 

M  =  1000  (M  ~  1000000,  MDC  =  600,  MXVI  =  1018> 


ROMAN   NOTATION  81 

To  express  other  numbers  these  same  letters  are  combined 
according  to  the  following 


Principles  of  Roman  Notation 

16.    1.    Placing  a  letter  after  one  of  greater  value  adds 
its  value  to  that  of  the  greater. 

2.  Placing  a  letter  before  one  of  greater  value  sub- 
tracts its  value  from  that  of  the  greater. 

3.  Placing  a  letter  between  two  letters  of  greater 
value  subtracts  its  value  from  their  sum. 

4.  Repeating  a  letter  repeats  its  value. 

5.  Placing  a  bar  over  a  letter  multiplies  the  value  of 
the  letter  by  1000. 


ILLUSTRATIONS 

17.    l.    X  =  10,  V  =  5,  X V  =  10  +  5  =  15.     Which  prin- 
ciple does  this  illustrate  ? 

2.  V  =  5,  I  =  1,  I V  =  5  —  1  =  4.     Which  principle  does 
this  illustrate  ? 

3.  C  -  100,  L  =  50,  X  =  10,  CXL  =  100  +  50  -  10  =  140. 
Which  principle  does  this  illustrate? 

4.  X  =  10,  XXX  =  10  +  10  +  10  =  30.     Which  principle 
does  this  illustrate  ? 

5.  D  =  500.      D  =  500000.     Which  principle  does  this 
illustrate  ? 

6.  CCCLX  =  360.     Which  principle  ? 

7.  MOM  =  1900.     Which  principle  ? 

8.  MDCLXVI  =  1666.     Which  principle  ? 

9.  Write    numbers   to   illustrate    all    the    principles   of 
Roman  notation. 

10.    Express  in  Roman  notation  all  numbers  from  1  to  100. 


82 


PRIMARY   ARITHMETIC 


18.    Read  : 

1.  XLV.  6.  MCIV. 

2.  CDII.  7.  DCCVI. 

3.  MI.  8.  MXIX. 

4.  XIX.  9.  DCX. 

5.  LXXXVI.  10.  CDLI. 

Write  in  Roman  notation  : 

1.  284  5.  319 

2.  98  6.  1,515 

3.  1,013  7.  745 

4.  56  8.  47 


11.  DCXCIV. 

12.  MCCV. 
is.  CCXI. 
14.  MMV. 
is.  DLXVI. 

9.  2,870 

10.  837 

11.  1,400 

12.  245 


NOTATION  OF  FEDERAL  MONEY 

19.    Federal  Money  is  the  money  used  in  the  United  States. 
10  mills  =  1  cent.      Mills  are  not  coined.      The  smallest 
coin  used  is  the  cent.     Cents  are  written  ct.  or  tf. 

100  cents  =  1  dollar,  written  $1.  When  dollars  and  cents 
are  written  together,  a  period,  called  the  decimal  point,  is 
placed  between  them.  Thus,  four  dollars  and  sixty-seven 
cents  is  written  $4.67. 

The  first  two  places  at  the  right  of  the  point  are  occupied 
by  cents,  the  third  place  by  mills. 

Nine  cents  four  mills  is  written  $.094. 
Four  dollars  sixty-five  cents  three  mills  is  written  $4.653. 
Copy  and  read  : 

1.   $     8.40  2.      $16.30  3.   $   92.003 

$  17.03  $  9.  $       .105 

$     2.842  $     .087  $256.428 

$200.504  $4007.91  $  94.02 

Write  in  figures : 

1.    Seventy  dollars  twenty-six  cents. 


ADDITION 


20.  Addition  is  the  process  of  uniting  two  or  more  like 
numbers  into  one  number.     Thus,  2  and  5  are  7. 

21.  The  numbers  added  are  Addends.     Thus,  3  and  10  are 
13  ;  3  and  10  are  the  addends. 

22.  The  result  of  addition  is  the  Sum.     Thus,  8  books 
and  7  books  are  15  books  ;  15  is  the  sum. 

The  addends  and  sum  are  called  the  terms  of  Addition. 

23.  The  Sign  of  Addition  is  a  vertical  cross  placed  between 
the  addends.     Thus,  5  +  9  are  14. 

The  sign  =  means  are  or  equals.     Thus,  8  +  3  =  11. 
What  kind  of  numbers  can  be  added  ? 


45599 
2  :L  ^  0»  5 

67899 
I  i  £  S.  5 
67891 
1  1  1  *  J 
67689 
£  1  1  1  J[ 

83 


24. 

Add 

at  sight  : 

2 

6 

7 

3 

5 

3 

1 

1 

2 

3 

4 

5 

1 

3 

4 

4 

2 

3 

4 

5 

2 

3 

8 

1 

2 

3 

4 

5 

7 

9 

8 

7 

84  PRIMARY   ARITHMETIC 


2 

3 

4 

5 

6 

7 

8 

9 

3 

4 

5 

5 

2 

5 

4 

4 

2 

3 

4 

9 

6 

7 

7 

8 

4 

5 

6 

5 

6 

6 

5 

7 

25.   Oral. 

1.  Ruth  had  7  cents  and  earned  8  cents  more.     How 
many  cents  had  she  then  ? 

2.  We  had  8  books  in  our  library  and  bought  10  more. 
How  many  have  we  now  ? 

3.  Five  pupils  are  absent  from  a  class  and  12  are  present. 
How  many  pupils  are  there  in  the  class  ? 

4.  Edward  had  10  cents  in  his  bank  and  put  in  6  more. 
How  much  money  has  he  now  ? 

5.  There  are  12  pears  in  one  box  and  10  in  another. 
How  many  in  both  boxes  ? 

6.  Albert  spent  8  cents  for  a  ball,  4  cents  for  a  pencil, 
and  12  cents  for  a  writing-book.     How  much  did  he  pay 
for  all  ? 

7.  Willard  had  7  marbles  in  one  bag  and  12  in  another. 
How  many  had  he  in  both  bags  ? 

8.  A  boy  sold  a  pair  of  skates  for  20  cents,  which  was 
10  cents  less  than  they  cost.     What  did  they  cost  ? 

9.  John  paid  5  cents  for  paper,  2  cents  for  pens,  and  4 
cents  for  pencils.     How  many  cents  did  he  pay? 

10.  Will  has  six  marbles  and  Frank  11.     How  many  have 
both? 

11.  Mary  bought  a  nine-cent  ball  and  a  twelve-cent  pine- 
apple.    How  much  did  she  pay  for  both  ? 

12.  Susie  had  12  violets  and  picked  9  more.     How  many 
had  she  then  ? 


ADDITION  85 

13.  Three  boys  went  fishing.     One  caught  15  fish,  another 
11,  and  the  other  16.     How  many  fish  were  caught  ? 

14.  A  boy  spent  8  cents  for  a  slate  and  21  cents  for  a  book. 
How  much  did  both  cost  ? 

15.  A  boy  had  a  nickel.     He  found  a  dime,  and  his  mother 
gave  «him  8  cents.     How  many  cents  did  he  then  have  ? 

26.    Oral.     Add: 
i.   3     2.   5     3.   4     4.   5     5.    6     6.   7     7.   3     8.   7     9.   7 

268785054 
6^82938923 

10.  6+5  +  4=?  8  +  5  +  3  =  ?  7  +  6+8  =  ? 

11.  4+6  +  3  =  ?  7  +  9  +  8  =  ?  5  +  5+5  =  ? 

12.  6+3  +  8  =  ?  5  +  4  +  3  =  ?  7  +  7+9  =  ? 
is,  6+6  +  8  =  ?  9  +  8  +  9  =  ?  6  +  5+4  =  ? 

14.  10+    5  +  0  =  ?          8  +  9  +  7  =  ?          7  +  1+8  =  ? 

15.  2  +  10  +  9  =  ?          4  +  8  +  7  =  ?          5  +  1  +  11  =  ? 

0 

16.  A  grocer  sold  a  melon  for  25  cents  and  a  basket  of 

grapes  for  15  cents.     How  much  did  he  receive  for  both  ? 

17.  A  boy  is  7  years  old.     His  sister  is  4  years  older,  and 
his  father  25  years  older  than  his  sister.     How  old  is  his 
father  ? 

18.  Mr.  A  lives  10  miles  east  of  a  village,  and  Mr.  B  17 
miles  west.      How  many  miles  from  Mr.  A's  to  Mr.  B's  ? 

19.  Mary  had  15  cents,  and  John  25  cents.     How  many 
had  both  ? 

20.  A  drover  bought  8  cows,  5  horses,  and  10  sheep.     How 
many  animals  did  he  buy  ? 

21.  Fred  paid  10  dollars  for  a  goat  and  12  dollars  for  a 
cart.     How  much  did  both  cost  him  ? 


86  PRIMARY  ARITHMETIC 


27. 

Written. 

Add: 

i.  3 

2. 

7 

3. 

8        4. 

7 

5. 

6 

6 

.  7 

7.    8         8. 

3 

4 

6 

9 

4 

0 

5 

5 

9 

5 

4 

2 

3 

9 

4 

7 

8 

9 

3 

5 

8 

5 

6 

6 

7 

In 

adding 

f  columns  like 

the 

1st, 

say  9—14—18  —  21,  not 

9  and 

5  are  14  and 

4  are  18,  etc. 

9.    7 

10.   6 

11. 

4 

12.    5 

13. 

4 

14. 

7 

15.    8 

16.    9     17. 

5 

5 

5 

5 

9 

3 

5 

7 

7 

4 

3 

4 

6 

8 

9 

6 

5 

6 

3 

0 

9 

0 

6 

2 

2 

0 

4 

9 

6 

3 

8 

5 

7 

3 

7 

2 

8 

18.    3 

19.    9 

20. 

2 

21.    8 

22. 

2 

23. 

6 

24.    2 

25.    3     26. 

5 

9 

7 

8 

5 

9 

9 

9 

5 

5 

8 

5 

7 

0 

6 

5 

7 

7 

8 

5 

3 

9 

7 

5 

8 

6 

0 

r- 
< 

7 

2 

5 

4 

8 

7 

8 

8 

7 

4 

0 

7 

3 

4 

6 

••     4 

7 

6 

2 

4 

2 

2 

rr 

2 

9 

6 

3 

28. 

i.  13 

+  5 

6.  13 

+  6 

11. 

14 

+  7 

16.    14  + 

8 

2.  23 

+  5 

7.  23 

+  6 

12. 

24 

+  7 

17.  24  + 

8 

3.  33 

+  5 

8.  33 

+  6 

13. 

34 

+  7 

18.  34  + 

8 

4.  43 

+  5 

9.  43 

+  6 

14. 

44 

+  7 

19.  44  + 

8 

5.  53 

+  5 

10.  53 

+  6 

15. 

54 

+  7 

20.  54  + 

8 

21.  A  boy  rode  his  wheel  23  miles  on  Monday,  10  miles  on 
Tuesday,  and  5  miles  on  Wednesday.     How  many  miles  did 
he  ride  in  the  three  days  ? 

22.  A  farmer  purchased  a  cow  for  35  dollars,  and  a  pig  for 
8  dollars.     What  was  the  cost  of  both  ? 


ADDITION  87 

23.  Iii  a  certain  school  28  pupils  were  present,  5  were 
absent  on  account  of  sickness,  and  4  were  absent  for  other 
reasons.     How  many  pupils  belonged  to  the  school  ? 

24.  A  farmer  sold  25  bushels  of  apples  to  one  man,  10  to 
another,  and  8  to  another.     How  many  bushels  did  he  sell? 

25.  John  had  40  cents  in  his  bank.     He  added  8  cents  on 
Monday,  and  10  cents  on  Wednesday.     How  much  money 
had  he  then  in  his  bank  ? 

26.  A  man  paid  for  paint  56  dollars,  and  for  labor  10  dol- 
lars.    How  much  did  he  pay  for  both  ? 

27.  Bought  sheep  for  50  dollars,  turkeys  for  12  dollars, 
and  chickens  for  8  dollars.     How  much  did  they  cost  ? 

28.  A  man  in  repairing  his  house  paid  35  dollars  for  lum- 
ber, 8  dollars  for  paint,  2  dollars  for  nails,  and  10  dollars  for 
labor.     What  was  the  cost  of  his  repairs  ? 

29.  How  many  fish  did  Mr.  A  catch  in  4  days  if  he  caught 
12  the  first  day,  8  the  second,  9  the  third,  and  7  the  fourth  ? 

30.  A  girl  spent  for  car  fare  5  cents,  for  pencils  4  cents, 
for  paper  8  cents,  for  ribbon  10  cents,  for  lunch  15  cents, 
and  had  9  cents  left.     How  much  money  had  she  at  first  ? 

31.  John  has  20  marbles,  Henry  4  more  than  John,  and 
Fred  5  more  than  Henry.     How  many  marbles  has  Fred? 


Add: 

32. 

42 

33. 

52 

34.     62 

35.     72 

36. 

82 

37.     92 

9 

9 

9 

9 

9 

9 

38.    34          39.     54          40.     74          41.     94          42.     44          43.     64 

888888 

44.    28          45.     48          46.     68          47.     38          48.     58          49.     78 

777777 


88  PRIMARY  ARITHMETIC 

50.    24          51.     34          52.     54  53.     74          54.     44  55.     64 

888888 
888888 


29.   Written.  — i.   Add  4150 

and  5827 

7  units  and  0  units  are  how  many  units  ? 
2  tens  and  5  tens  are  how  many  tens  ? 

8  hundreds  and  1  hundred  are  how  many  hundreds  ? 

5  thousands  and  4  thousands  are  how  many  thousands  ? 
All  the  above  work  might  be  expressed  thus : 

4150 


=  9977    Sum. 

2.  Three  or  more  numbers  may  be  added  in  the  same  way, 

thus  : 

543,122  ] 

12,367 
10,200 

1,100  J 
566,789    Sum. 

3.  Add: 

763  How  should  we  write  the  addends  so  that 

528  we  may  easily  add  units  and  units,  tens  and 

659  tens,  etc.  ? 
435 

5  units  +  9  units  +  8  units  -f  3  units  are  how  many  units  ? 

25  units  make  how  many  tens  and  how  many  units  over  ? 
Put  the  5  units  under  units'  column,  and  add  2  to  tens' 
column. 


ADDITION  89 

2  tens  +  3  tens  4-  5  tens  +  2  tens  +  6  tens  are  how  many 
tens  ?  18  tens  make  how  many  hundreds  and  how  many 
tens  over  ? 

Put  the  8  tens  under  tens'  column,  and  add  1  to  hundreds' 
column.  1  hundred  -f-  4  hundreds  -f-  6  hundreds  +  5  hun- 
dreds +  7  hundreds  are  how  many  hundreds  ?  23  hundreds 
make  how  many  thousand  and  how  many  hundreds  over  ? 

Put  3  hundreds  under  hundreds'  column  and  2  thousands  in 
thousands'  column  in  the  sum.  What  would  you  do  with  2 
thousands  if  there  were  thousands  in  the  addends  ? 

30.  From  the  foregoing  examples  we  may  make  the  fol- 
lowing 


Rule  for  Addition 

1.  Write  the  addends  so  that  the  figures  in  units' 
place  in  all  the  addends  shall  stand  in  the  same  column. 

2.  Add  the   figures  in  the  right-hand  column.     If 
the  sum  is  less  than  ten,  write  it  under  units'  column. 
If  it  is  ten  or  more,  divide  it  by  ten,  write  the  remain- 
der under  units'  column,  and  add  the  quotient  with  the 
figures  in  tens'  column.     Proceed  in  this  way  till  all 
the  columns  have  been  added. 

3.  Whenever  the  sum  of  any  column  is  10  or  more, 
divide  it  by  10,  put  the  remainder  under  the  column 
added,  and  add  the  quotient  with  the  next  column  to 
the  left. 

4.  To  add  Federal  Money,  write  the  addends  so  that 
all  the  decimal  points  shall  stand  in  the  same  column. 
Add  the  same  as  other  numbers,  and  place  the  deci- 
mal point  in  the  sum  under  the  decimal  points  in  the 
addends. 


90  PRIMARY   ARITHMETIC 


Proof  of  Addition 

1.    Add  the  numbers  in  a  different  order.     If  the  re- 
sults agree,  the  work  is  generally  correct.     Or, 
2.    Subtract  the  addends,  one  at  a  time,  from  the  sum. 
If  the  last  result  is  zero,  the  addition  is  correct. 

31.    Add: 

4.     36            5. 

25 

6.    96 

7.     25           8. 

87        9.    38 

70 

98 

39 

75 

96              49 

21 

76 

78 

84 

48              96 

84 

29 

54 

26 

93              44 

10.    28      11. 

639 

12.    1050 

is.      126 

14.    1115.85 

39 

874 

394 

149 

327.15 

76 

596 

769 

1260 

495.27 

42 

421 

564 

1004 

160.03 

89 

397 

285 

986 

598.09 

73 

269 

784 

24 

784.06 

15.     97      16. 

857 

17.      283 

18.    $208.40 

19.    $356.24 

98 

943 

2075 

32.03 

35.09 

79 

268 

298 

26..  07 

2.15 

68 

207 

963 

18.94 

30.05 

40 

976 

859 

236.29 

5.16 

87 

888 

876 

28.15 

304.29 

20.    2673 

21. 

837 

22.      628 

23.    8063 

846 

2964 

4307 

259 

1025 

418 

526 

8264 

92 

3825 

8279 

1287 

837 

842 

428 

428 

642 

29. 

4273 

3064 

ADDITION  91 


Add: 
24 


$26.43 

25.    $715.30 

26.    $165.00 

27.    $  20.863 

18.75 

21.86 

8.429 

129.40 

2.93 

9.246 

113.82 

5208.00 

4.10 

10.163 

6.804 

.926 

128.06 

7.208 

39.625 

128.753 

563.13 

516.00 

11.31 

37.15 

28.00 

8.096 

476.203 

192.097 

28.  Add   seventeen   thousand,    nine   hundred   six ;     four 
thousand,  two  hundred  eighty-nine;  eight  hundred  twelve 
thousand,  seven  hundred  eight ;  six  hundred  two ;  forty-two 
thousand,  nine  hundred  two ;  twelve  thousand. 

29.  Find  the  sum  of  eleven  thousand,  six  hundred  seven- 
teen ;  sixty-eight ;  four  thousand,  twenty-five ;  two  thousand, 
three  hundred  nine ;  eighty-five  thousand. 

30.  A  merchant's  sales  were  $2963.84  in  January,  $1463.27 
in   February,  $3846.25  in   March,  and  $2016.92  in  April. 
What  did  his  sales  amount  to  in  the  four  months? 

31.  Find  the  sum  of  all  the  numbers  between  and  includ- 
ing 167  and  174. 

32.  A  man  had  $170  in  his  pocket,  which  was  $70.75  less 
than  he  had  in  his  safe.     How  much  money  had  he  in  the 
safe? 

33.  Add  nine  dollars  six  cents;  fifteen  dollars  seventy- 
two  cents;  sixty  dollars  eighty-seven  cents;  fifty-nine  cents; 
four  dollars  five  cents ;  two  hundred  dollars  thirteen  cents. 

34.  Add  3160,  4980,  7592,  8324,  6958. 

35.  Add  21563,  74321,  58026,  79532,  43984. 

36.  Add  32162,  19073,  76352,  698725,  49623. 

37.  Add  36,  512,  7198,  41960,  75,  34,  812,  916. 


92  PRIMARY   ARITHMETIC 

38.  Add  $5.28,  $13.936,  $17.84,  $16.05,  $28.006. 

39.  Add  $28.75,  $19.87,  $16.97,  $14.82,  $17.64,  $18.26, 
$19.78. 

40.  Add  28,  97,  386,  9428,  359601,  4289,  86. 

41.  69872,  594760,  653051,  21876,  394321. 

42.  Add  8  thousand  312  ;    25  thousand  906  ;  215  thou- 
sand 7  hundred  8 ;   15  thousand  9  hundred  15  ;  56  thousand 
2  hundred  74 ;  328  thousand  906. 

43.  Add  5  dollars  18  cents  5  mills;  28  dollars   1   cent; 
19  dollars  24  cents  5  mills;  17  dollars  18  cents;  84  dollars 
2  cents  9  mills ;  29  dollars  8  cents  ;  328  dollars  50  cents  4 
mills. 

PROBLEMS   IN    ADDITION 

32.    l.    Georgie  has  18  peaches,  and  Donald  23  peaches. 
How  many  have  both? 

2.  In   a  schoolroom  are    24  boys   and   17   girls.     How 
many  children  are  there  in  all  ? 

3.  A  farmer  has  21  sheep  in  one  pasture,  32  in  another, 
and  45  in  a  third.     How  many  sheep  has  he  in  all? 

4.  A  boy  picked  up  26  bushels  of  potatoes  on  Monday, 
29   bushels    on  Tuesday,    and    32  bushels    on    Wednesday. 
How  many  bushels  did  he  pick  up  in  all  ? 

5.  Frank  paid  35  cents  for  a  knife,  45  cents  for  a  ham- 
mer, and  50  cents  for  a  saw.     How  much  did  he  pay  for  all  ? 

6.  Mr.  Smith  has  42  apple  trees,  24  pear  trees,  16  plum 
trees,  and  19  cherry  trees.     How  many  fruit  trees  has  he  ? 

7.  John  picked  23  quarts  of  berries,  Henry  19  quarts, 
Sarah  26  quarts,  and  Mildred  12  quarts.     How  many  quarts 
did  they  all  pick? 


PROBLEMS   IN   ADDITION  93 

8.  Charles  lives  84  miles  west  of  Chicago,  arid  William 
49  miles  east.     How  far  apart  do  they  live  ? 

9.  In  a  yard  are  56  hens,  24  ducks,  28  turkeys,  and  18 
geese.     How  many  fowls  in  the  yard  ? 

10.  A  lady  bought  eggs  for  45  cents,  sugar  for  75  cents, 
tea  for  68  cents,  and  meat  for  32  cents.     How  much  did  she 
pay  for  all  ? 

11.  Mary  is  10  years  old,  Clara  is  5  years  older  than  Mary, 
and  their  brother  is  as  old  as  both  of  them  together.     What 
is  the  sum  of  their  ages  ? 

12.  On  one  side  of  a  street  are  62  houses,  and  on  the  other 
59  houses.     How  many  houses  are  on  the  street? 

13.  If  a  boy  is  10  minutes  late  at  school  on  Monday,  8 
minutes  on  Tuesday,  15  minutes  on  Wednesday,  7  minutes 
on  Thursday,  and  12  minutes  on  Friday,  how  many  minutes 
does  he  lose  in  the  week? 

14.  Three  boys    went  fishing,  and  caught  16  perch,  19 
pickerel,  and  8  black  bass.     How  many  fish  did  they  catch 
in  all? 

15.  Two  trains  starting  from  the  same  place  run  two  days 
in  opposite  directions.     One  runs  530  miles  the  first  day  and 
525  miles  the  second,  while  the  other  runs  492  miles  the  first 
day  and  510  miles  the  second.      How  far  apart  are  they  at 
the  end  of  the  two  days  ? 

16.  A  man  bought  coal  for  $5.60,  wood  for  $3.45,  and  a 
stove  for  $45.     What  was  the  whole  cost? 

17.  There   are  112  bushels  of  wheat  in  one  bin,  175  in 
another,  and  234  in  the  third.     How  many  bushels  in  all? 

18.  There  are  218  pages  in  my  reader,  245  pages  in  my 
arithmetic,  and   195  pages  in   my  geography.      How  many 
pages  in  the  three  books  ? 


SUBTRACTION 


33.  Subtraction  is  the  process  of  finding  the  difference  be- 
tween two  like  numbers.     Thus,  21  less  7  =  14 ;  13  ct.  less 
5  ct.  =  8  ct. 

34.  The  number  from  which  we  subtract  is  the  Minuend. 
Thus,  15  less  9=6;  15  is  the  minuend.     The  number  sub- 
tracted is  the  Subtrahend.     Thus,  12  cents  less  5  cents  =  7 
cents ;   5  cents  is  the  subtrahend. 

35.  The  result  of  subtraction  is  called  the  Difference  or 
Remainder.       Thus,  25  miles  less  15  miles  =  10  miles;    10 
miles  is  the  difference  or  remainder.     The  minuend,  subtra- 
hend, and  remainder  are  called  the  Terms  of  Subtraction. 

The  Sign  of  Subtraction  is  a  short  horizontal  line  placed 
before  the  subtrahend ;  thus,  12  birds  —  4  birds  =  6  birds. 

What  kind  of  numbers  can  be  subtracted  ?  How  does  the 
minuend  compare  with  the  subtrahend  ?  With  the  remainder? 


36. 

Subtract  at  sight  : 

i. 

14- 

4 

11. 

12 

-5 

21. 

16- 

10 

31. 

8- 

6 

2. 

12- 

7 

12. 

16 

-8 

22. 

18- 

8 

32. 

7- 

1 

3. 

15- 

9 

13. 

13 

-6 

23. 

19- 

5 

33. 

9- 

0 

4. 

17- 

8 

14. 

11 

-8 

24. 

7  — 

6 

34. 

11- 

3 

5. 

9- 

5 

15. 

16 

-5 

25. 

10- 

2 

35. 

10- 

6 

6. 

11- 

4 

16. 

7 

-4 

26. 

11- 

10 

36. 

15- 

9 

7. 

13- 

3 

17. 

11 

-6 

27. 

15- 

15 

37. 

20- 

10 

8. 

7- 

7 

18. 

9 

-2 

28. 

13- 

2 

38. 

13- 

7 

9. 

15- 

5 

19. 

8 

-5 

29. 

14- 

7 

39. 

15- 

3 

10. 

17- 

10 

20. 

7 

-3 

30 

16- 

2 

40. 

14- 

3 

94 


SUBTRACTION  95 


41. 

7 

+  ?  = 

14 

51. 

15  + 

?  =  20 

61. 

18 

-  9  = 

? 

42. 

8 

+  ?  = 

11 

52. 

11  + 

?  =  15 

62. 

13 

-11  = 

? 

43. 

6 

+  ?  = 

15 

53. 

9  + 

?  =  14 

63. 

15 

-10  = 

? 

44. 

5 

+  ?  = 

11 

54. 

8  + 

?  =  15 

64. 

17 

-10  = 

? 

45. 

7 

+  ?  = 

16 

55. 

7  + 

?  =  12 

65. 

? 

+  5  = 

11 

46. 

8 

+  ?  = 

16 

56. 

8  + 

?  =  11 

66. 

? 

+  7  = 

16 

47. 

6 

+  ?  = 

9 

57. 

17- 

8  =  ? 

67. 

? 

+  5  = 

16 

48. 

7 

+  ?  = 

15 

58. 

14- 

5  =  ? 

68. 

? 

+  6  = 

19 

49. 

11 

4-  ?  = 

14 

59. 

17- 

5  =  ? 

69. 

? 

+  4  = 

13 

50. 

13 

+  ?  = 

16 

60. 

20- 

9  =  ? 

70. 

? 

+  6  = 

11 

37.   Oral. 

1.  Frank  had  15  cents  in  his  bank  and  took  out  5  cents. 
How  many  cents  remained  ? 

2.  There  were  13  sparrows  upon  a  limb,  and  5  flew  away. 
How  many  sparrows  remained  on  the  limb  ? 

3.  A  farmer  planted  potatoes  and  corn  in  a  field  contain- 
ing 12  acres.     He  planted  potatoes  in  7  acres.     In  how  many 
acres  was  corn  planted  ? 

4.  John  had  14  marbles  and  gave  away  6  of  them.     How 
many  had  he  left  ? 

5.  Frank   lives  12  blocks  east   of   the   schoolhouse,  and 
Henry  5  blocks  east.     How  many  blocks  between  Frank's 
home  and  Henry's  home  ? 

6.  In  a  garden  there   are  20  rose  bushes.     Only  10  of 
them  bear  red  roses.      How  many  bushes  do  not  bear  red 
roses  ? 

7.  Mary  added  two  numbers,   and   her  answer  was  18. 
The  smaller  number  was  8.      What  was  the  larger  ? 

8.  A  farmer  having  17  cows  sold  6  of  them.      How  many 
remained  ? 

9.  A  clerk  earns  14  dollars  a  week  and  spends  6  dollars. 
How  much  does  he  save  each  week  ? 


96  PRIMARY   ARITHMETIC 

10.  Mary  bought  ribbon  for  10  cents  and  paper  for  5  cents. 
How  much  had  she  remaining  from  20  cents  ? 

11.  From  a  basket  containing  16  oranges,  7  were  taken. 
How  many  were  left  ? 

12.  James  is  7  years  younger  than  his  brother,  who  is  15 
years  old.     How  old  is  James  ? 

13.  If  you  have  19  cents  and  spend  10  cents,  how  much 
have  you  left  ? 

14.  A  boy  sold  for  12  cents  a  ball  that  cost  him  20  cents. 
How  much  did  he  lose  ? 

15.  How  much  more  is  20  than  11  ? 

16.  Tom  has  20  marbles,  and  Edward  11.     How  many  has 
Tom  more  than  Edward  ? 

17.  If  you  give  15  cents  in  payment  for  a  slate  worth  20 
cents,  how  much  do  you  still  owe  ? 

18.  Nell  had  21  chickens,  but  a  dog  killed  10  of  them. 
How  many  were  left  ? 

19.  Lucy  is  20  years  old,  and  her  sister  6  years  younger. 
How  old  is  her  sister  ? 

20.  John'had  $20.     He  spent  $10  for  a  coat  and  $3  for  a 
hat.     How  much  had  he  left  ? 

21.  A  pole  is  19  feet  long.     I  cut  off  4  feet  at  one  time 
and  6  feet  at  another.     How  many  feet  were  left  ? 

38.    Oral.     Subtract : 
i.    38       2.  48       3.  58       4.  88       5.  68       6.  78       7.  98 

7  7  JT  _T_  _1_  _T_  _7 

8.   13       9.   23     10.   53     11.    73     12.   83     13.   63     14.  43 
_5  _5          _5          _5          _5  _5          _5 

15.   26     16.    36     17.    56     18.    66     19.   46     20.   76     21.  96 


SUBTRACTION  97 

22.     21      23.     31      24.    41      25.     71      26.     91      27.    51      28.    81 

9999999 


29. 

15- 

3 

33. 

55- 

3 

37. 

14- 

7 

41. 

54- 

7 

30. 

25- 

3 

34. 

65- 

3 

38< 

24- 

7 

42. 

64- 

7 

31. 

35- 

3 

35. 

75- 

3 

39. 

34- 

7 

43. 

74- 

7 

32. 

45- 

3 

36. 

85- 

3 

40. 

44- 

7 

44. 

84- 

7 

45.  Subtract  6  from  each  of  these  numbers : 

15,     25,     35,    45,     55,     65,     75,     85,     95. 

46.  3  +  6  +  5  +  8-10-?     8  +  6  +  5  +  5-8-? 

47.  There  are  45  pupils  in  our  class.     8  are  absent.     How 
man}7'  are  present  ? 

48.  A  man  earns  $  56  a  month.     He  pays  $  7  a  month  for 
rent.     How  much  is  left  ? 

49.  51  birds  were  on  a  tree.     7  flew  away.     How  many 
remained  ? 

50.  A  lady  had  54  pounds  of  butter  in  a  tub,  and  used  7 
pounds.     How  many  pounds  remained  in  the  tub  ? 

51.  Mr.  R.  had  42  animals  in  a  field.      5  of  them  were 
horses,  and  the  rest  cows.     How  many  were  cows  ? 

52.  Ella  had  48  cents.     She  gave  5  to  Mary  and  4  to  Lucy. 
How  many  had  she  left  ? 

NOTE.  —  Subtract  5  from  48,  then  4  from  the  result. 

53.  Will  had  53  marbles  and  gave  9  to  Max  and  8  to  Fred. 
How  many  had  he  left  ? 

39.    1.    From  9867 
take     4263 

7  units  less  3  units  are  how  many  units  ?  Write  4  units 
under  units'  column. 

6  tens  —  6  tens  =  how  many  tens  ?  Write  0  under  tens' 
column. 


98  PRIMARY   ARITHMETIC 

8  hundreds  —  2  hundreds  =  how  many  hundreds  ?     Write 

6  hundreds  under  hundreds'  column. 

9  thousands  —  4  thousands  =  how  many  thousands  ?    Write 
5  thousands  under  thousands'  column. 

All  this  work  may  be  expressed  thus : 

9867  Minuend. 
-4263  Subtrahend. 
=  5604  Remainder. 
2.    From  4285 
take       597 

From  5  units  take  7  units.  Can  it  be  done  ?  From  8 
tens  take  1  ten  and  change  the  1  ten  to  units.  It  equals 
how  many  units?  Add  10  units  to  5  units-  How  many 
units  does  it  make  ?  From  15  units  take  7  units.  How 
many  units  are  left  ?  Write  8  units  under  units'  column. 

Since  you  have  taken  1  ten  from  8  tens  in  the  minuend, 
how  many  tens  are  left  ?  From  7  tens  take  9  tens.  Can  it 
be  done  ?  From  2  hundreds  take  1  hundred  and  change  it 
to  tens.  1  hundred  =  how  many  tens  ?  Add  10  tens  to 

7  tens.     How  many  tens  does  it  make  ?     From  17  tens  take 

9  tens.      How  many  tens  are   left  ?     Write   8  tens  under 
tens'  column. 

Since  you  have  taken  1  hundred  from  2  hundreds,  how 
many  hundreds  are  left  in  the  minuend  ?  From  1  hundred 
take  5  hundreds.  Can  it  be  done  ?  From  4  thousands  take 
1  thousand.  One  thousand  =  how*  many  hundreds  ?  Add 

10  hundreds  to  1   hundred.      How  many  hundreds  does  it 
make  ?     From  11  hundreds  take  5  hundreds.     How  many 
hundreds    are   left  ?     Write    6   hundreds   under   hundreds' 
column. 

Since  you  have  taken  1  thousand  from  4  thousands,  how 
many  thousands  are  left  ?  Write  3  thousands  in  thousands' 
place  in  the  remainder. 


SUBTRACTION  99 

All  this  work  may  be  expressed  thus : 
4285  Minuend. 

597  Subtrahend. 
=  3688  Remainder. 

40.    From  the  examples  given  above  we  may  make  the 
following 


Rule  for  Subtraction 

1.  Write  the  subtrahend  under  the  minuend  so  that 
units  shall  come  under  units. 

2.  From  units  take  units,  from. tens  take  tens,  and 
so  on  till  each  figure  of  the  subtrahend  has  been  sub- 
tracted from  the  figure  above  it,  writing  the  remainder, 
every  time,  below  the  figures  subtracted. 

3.  Whenever  a  figure  of  the  minuend  is  less  than 
the  figure  of  the  subtrahend  below  it,  take  1  from  the 
next  figure  to  the  left  in  the  minuend,  and  add  10  to 
the  figure  which  is  too  small.     Then  subtract  the  sub- 
trahend figure  from  the  sum  obtained. 

4.  To  subtract  Federal  money,  write  the  subtrahend 
under  the  minuend  so  that  the  decimal  point  of  the 
subtrahend  is  under  the  decimal  point  of  the  minuends- 
Then  subtract  the  same  as  other  numbers. 


41.  l.  12  —  ?  =  7  ?  Which  terms  of  subtraction  are  given 
in  this  question  ?  Which  term  are  you  asked  to  find  ?  How 
do  you  find  it  ?  When  the  minuend  and  remainder  are  given, 
how  can  the  subtrahend  be  found  ? 

2.  ?  —  5  =  7  ?  Which  terms  are  given  ?  Which  term  are 
you  to  find  ?  How  do  you  find  it  ?  When  the  subtrahend 
and  remainder  are  given,  how  can  the  minuend  be  found  ? 


100  PRIMARY   ARITHMETIC 

42.    The  answers  to  these  questions  give  us  the  following 


Proof  of  Subtraction 

1.  Subtract  the   remainder  from  the   minuend.     If 
the  result  is  the  same  as  the  subtrahend,  the  subtrac- 
tion is  correct.     Or, 

2.  Add  the  subtrahend  and  remainder.     If  the  sum 
is  the  same  as  the  minuend,  the  subtraction  is  correct. 


43.    Subtract: 
l.      2819 
674 


2. 


8203 
1276 


3.     4295 
597 


4. 


7306 

1807 


5. 


2763 

1289 


6.    37284 

9287 


7.    36801 
18463 


8.   18003 
921 


9.    92874 
11392 


10.    94210 

8206 


13.    38264 

29842 


14.    19327 

8291 


u.   $2.156 
1.124 

21.   $34.28 
24.28 


18.   $35.283 
17.05 


11.   42840 
38706 

is.    92593 

87246 

19.    25.18 
1.155 


12.    98301 
26942 

16.    27075 
18092 


20.   $36.514 
16.827 


22.   $39.216 
27.134 


23.    $17.804 
16.752 


24.   $75.005 
24.325 


25.  From  seventeen  thousand  sixteen,  take  nine  thousand 
four  hundred  eighty-seven. 

26.  From  seventy-two  thousand  three  hundred  eleven,  take 
forty-six  thousand  nine  hundred  sixty-one. 

27.  Take  eight  thousand  four,  from  thirty  thousand. 


SUBTRACTION  101 

28.  Find   the  difference  between  sixteen  thousand   four 
hundred  seventy-five,  and  twenty  thousand  seven  hundred 
twenty-seven. 

29.  The  minuend  is  7026  and  the  subtrahend  987.     Find 
the  difference. 

30.  Find  the  difference  between  9284  and  13,4110 

31.  $4216.56-11874.92  =  ? 

32.  $149.725-169.417=  ? 

33.  Take  sixteen  thousand  eight  hundred  seventeen,  from 
twenty-four  thousand  five  hundred  forty-one. 

34.  The  difference  is  8037.     The  minuend  is  19,406.     Find 
the  subtrahend. 

35.  Take   seventy-six   dollars   four  "cents  two  mills,  from 
one  hundred  two  dollars  nine  mills. 

36.  From  sixty-five  thousand  three  hundred  sixteen,  take 
twenty-four  thousand  forty. 

37.  Take  $86. 215  from  $900. 09. 

38.  What  must  be  added  to  $.67  to  make  $ 3  ? 

39.  From  a  farm  of  263  acres  of  land  97  acres  were  sold. 
How  much  was  left  ? 

40.  A   man  had  $279,   and  spent  $129.64.     How  much 
had  he  left? 

41.  From  a  cask  of  vinegar,  containing  44  gallons,  17  gal- 
lons leaked  out.     How  many  gallons  remained  ? 

42.  From  a  box  containing  200  oranges,  127  were  sold. 
How  many  oranges  remained  ? 

43.  A  farmer  having  250  acres  of  land,  sold   87  acres. 
How  many  acres  did  he  have  left  ? 

44.  Two  boys  start  together  and  run  in  the  same  direction. 
How  far  apart  are  they  when  one  has  run  192  yards  and  the 
other  156  yards  ? 

45.  There  were  83  sparrows  on  a  limb,  and  34  flew  away. 
How  many  remained  ? 


102  PRIMARY  ARITHMETIC 

46.  A  boy  having  $  2  spent  $  .75  for  a  pair  of  skates.    How 
much  had  he  left  ? 

47.  Gene  vie  ve  had  $1,  and  gave  Edith  37  cents.      How 
much  had  she  left  ? 

48.  There  are  49   eggs  in  a  basket.      How  many  more 
should  be  put  in  to  make  144  eggs  in  all  ? 

49.  John  picked  40  quarts  of  berries,  and  James  picked  13 
quarts  less  than  John.     How  many  quarts  did  James  pick  ? 

REVIEW   PROBLEMS 
ADDITION   AND    SUBTRACTION 

44.  1.  A  farmer,  having  456  bushels  of  corn,  sold  84 
bushels  to  one  man  and  135  bushels  to  another.  How  many 
bushels  did  he  have  left  ? 

2.  A  man  started  to  walk  112  miles  in  three  days.     He 
walked  32  miles  the  first  day,  and  41  miles  the  second.     How 
far  must  he  walk  the  third  day  to  complete  the  journey  ? 

3.  I  bought  a  cow  for  $42,  another  for  $48,  and  a  third 
for  $56.     For  how  much  should  I  sell  them  to  gain  $28  ? 

4.  A  lady  bought  sugar  for  65  cents,  tea  for  55  cents, 
molasses  for  72  cents,  butter  for  84  cents,  Starch  for  25  cents, 
and  gave  in  payment  a  five-dollar  bill.     How  much  change 
should  she  receive  ? 

5.  John's  father  gave  him  $2.25,  and  his  uncle  gave  him 
$1.40.     He  earned  enough  besides  so  that  he  bought,  with 
the  whole,  a  suit  of  clothes  for  $8.     How  much  did  he  earn? 

6.  Two  vessels  start  from  points  850  miles  apart,   and 
sail  toward  each  other.     How  far  are  they  apart  when  one 
has  sailed  246  miles  and  the  other  352  miles  ? 

7.  A  man  sold  one  horse  for  $145  and  another  for  $182. 
On  the  first  he  gained  $  23,  and  on  the  second  $  36.     What 
was  the  cost  of  both  ? 


vT*  *A*K 

REVIEW^  PROBtgaaSITERSITY 

8.  A  boy  bought  apples  for  $.45  amFpuaiis  iU^HT.62,  and 
sold  them  all  for  $  1.50.     What  was  his  profit  ? 

9.  John  sold  62  newspapers,   Frank  48,  and  Henry  27 
less  than  both  of  them.     How  many  did  Henry  sell  ? 

10.  A  grocer  sold  butter  for  $45  and  cheese  for  $62.     On 
the  butter  he  lost  $  6  and  on  the  cheese  he  gained  $14.     What 
was  the  cost  of  both  ? 

11.  In  a  school  of  480  pupils,  13  were  absent  from  the 
primary  department,  11  from   the  junior,  and   9   from  the 
senior.     How  many  were  present  in  the  whole  school  ? 

12.  A  man  earning  $800  a  year  paid  $208  for  board,  $175 
for  clothes,  and  $266  for  other  purposes.     What  does  he 


save 


13.  Mr.  Clark's  age,  which  is  50  years,  is  17  years  more 
than  the   sum  of  the  ages  of  his  son  and  daughter.     His 
daughter  is  18  years  old.     How  old  is  his  son  ? 

14.  A  farmer  bought  a  barrel  of  flour  for  $6.35,  sugar  for 
$2.15,  coffee  for  $1.46,  tea  for  $1.20,  and  gave  in  payment 
$3.15  worth  of  butter  and  the  remainder  in  cash.     What 
did  he  pay  in  money  ? 

15.  The  sum  of  52  and  64  is  how  much  greater  than  the 
difference  between  124  and  69? 

16.  From  a  flock  of  320  sheep  were  sold  at  one  time  76 
and  at  another  112.     How  many  remained  ? 

17.  A  man   bought   148   bushels  of   potatoes  of  A,   216 
bushels  of  B,  183  bushels  of  C,  and  afterwards  sold  all  but 
137  bushels.     How  many  bushels  did  he  sell  ? 

18.  The  sum  of  three  numbers  is  342.     Two  of  the  num- 
bers are  84  and  96.     What  is  the  third  number  ? 

19.  A  farmer  having  215  acres  of  land,  used  21  acres  for 
corn,  36  for  oats,   29  for  barley,   18   for   potatoes,   52   for 
meadow,  and  the  rest  for  pasture.     How  many  acres  were 
used  for  pasture  ? 


MULTIPLICATION 


45.  Multiplication  is  finding  a  number  which  is  a  certain 
number  of  times  another  number.     Thus,  6  times  5  dollars 
=  30  dollars. 

46.  The  number  multiplied  is  the  Multiplicand.     Thus,  7 
times  9  =  63.     9  is  the  multiplicand. 

47.  The  number  by  which  we  multiply  is  the  Multiplier. 
Thus,  12  times  7  =  84.     12  is  the  multiplier. 

48.  The  result  of  multiplication  is  the  Product.     Thus,  6 
times  3  feet  =18  feet.     18  feet  is  the  product. 

49.  The  multiplicand,  multiplier,  and  product  are  called 
the  Terms  of  Multiplication. 

50.  The  Sign  of  Multiplication  is  an  oblique  cross  placed 
after  the  multiplicand.      Thus,  $12  x  6  means  6  times  $12. 

51.  A  number  that  is  applied  to  some  particular  things  or 
objects  is  a  Concrete  Number.    Thus,  10  cows,  5  books,  6  gal- 
lons. 

52.  A  number  that  is  not  applied  to  anything  is  an  Abstract 
Number.     Thus,  10,  5,  6. 

53.  The  product  is  always  the  same  kind  of  a  number  as 
the  multiplicand.     Thus,  12  pounds  x  3  =  36  pounds.     Both 
the  multiplicand  and  product  are  pounds. 

54.  The  multiplier  is  always  regarded  as  an  abstract  number. 

104 


MULTIPLICATION  105 

55.    Tell  products  at  sight : 


3 

4 

5 

9 

8 

4 

6 

5 

8 

6 

7 

8 

6 

5 

8 

8 

4 

3 

9 

5 

6 

3 

6 

7 

4 

0 

7 

2 

6 

4 

7 

6 

6 

0 

4 

10 

9 

3 

4 

10 

10 

11 

11 

12 

12 

8 

7 

10 

2 

7 

2 

7 

2 

7 

3 

5 

4 

5 

9 

7 

3 

4 

10 

8 

8 

5 

3 

9 

7 

5 

11 

3 

10 

11 

11 

12 

12 

9 

5 

4 

6 

8 

3 

8 

3 

8 

3 

9 

6 

4 

9 

3 

4 

10 

10 

11 

11 

12 

12 

10 

9 

12 

4 

9 

4 

9 

4 

9 

10 

10 

4 

6 

9 

4 

10 

10 

11 

3 

5 

7 

6 

10 

8 

5 

10 

5 

11 

11 

10 

12 

12 

8 

5 

8 

3 

10 

5 

11 

5 

10 

7 

9 

2 

«  7 

9 

3 

4 

8 

9 

5 

12 

4 

12 

12 

12 

7 

8 

9 

5 

12 

4 

11 

56. 

Oral. 

1. 

Multiply 

these 

numbers  by  6. 

By  ; 

8.     By 

9: 

r, 

q         4 

V9            T:, 

3, 

8, 

11,       5, 

10, 

12, 

2, 

6. 

2.  At  3  cents  each,  what  will  5  oranges  cost  ? 

3.  Fred  saves  8  cents  a  day.     How  much  can  he  save  in 
9  days  ? 


106  PRIMARY   ARITHMETIC 

4.  At  $  5  each,  what  will  11  sheep  cost  ? 

5.  Eight  five-cent  tablets  cost  how  much  ? 

6.  How  many  trees  must  I  plant  to  make  a  square  orchard 
with  7  trees  on  a  side  ? 

7.  At  $4  a  week,   how  much  will  a  man's  board  bill 
amount  to  in  11  weeks  ? 

8.  There  are  8  pints  in  a  gallon.     How  many  pints  in  9 
gallons  ? 

9.  There  are  4  pecks  in  a  bushel.     How  many  pecks  in  6 
bushels. 

10.  One  horse  eats  6  quarts  of  oats  a  day.     How  many 
quarts  will  10  horses  eat  in  a  day  ? 

11.  What  will  a"  dozen  oranges  cost  at  3  cents  each  ? 

12.  A  man  can  build  5  rods  of  fence  in  a  day.     How  many 
rods  can  he  build  in  12  days  ? 

13.  Cloves  cost  7  cents  an  ounce.      What  will  8  ounces 
cost  ? 

14.  How  many  quarts  of  water  will  be   contained  in  6 

8-quart  pails  ? 
i 

15.  On  a  card  are  6  rows  of  buttons  with  10  buttons  in  a 

row.     How  many  buttons  on  the  card  ? 

16.  James  has   7  marbles,  and  Henry  6   times  as  many. 
How  many  marbles  has  Henry  ? 

17.  At  5  cents  a  quart,  what  is  my  milk  bill  for  7  days,  if 
I  use  2  quarts  a  day  ? 

18.  A  steamer  travels  12  miles  an  hour.     How  far  can  she 
travel  in  6  hours  ? 

19.  There  are  4  pecks  in  a  bushel.     How  many  pecks  in 
12  bushels  ? 


MULTIPLICATION  107 

20.  John  has  2  cents,  Robert  twice  as  many  as  John,  and 
Will  3  times  as  many  as   Robert.     How  many  cents  has 
Will? 

21.  Ten  mills  make  one  cent.     How  many  mills  in  10 
cents  ? 

22.  At  $.05  a  quart,  what  will  be  the  cost  of  9  quarts  of 
bird  seed  ? 

23.  At  12  cents  a  quart,  what  will  10  quarts  of  molasses 
cost? 

57.    Multiply  4127 
by        6 

6  times  7  units  are  how  many  units  ?  42  units  equal  how 
many  tens  and  how  many  units  over  ?  Write  2  units  in 
units'  place  in  the  product,  and  add  the  4  tens  to  the  product 
of  tens. 

6  times  2  tens  are  how  many  tens  ?  12  tens  and  4  tens 
are  how  many  tens  ?  16  tens  equal  how  many  hundreds  and 
how  many  tens  over  ?  Write  6  tens  in  tens'  place  in  the 
product,  and  add  1  hundred  to  the  product  of  hundreds. 

6  times  1  hundred  are  how  many  hundreds  ?  6  hundreds 
and  1  hundred  are  how  many  hundreds  ?  Write  7  hundreds 
in  hundreds'  place  in  the  product. 

6  times  4  thousands  are  how  many  thousands  ?  24  thou- 
sands =  how  many  ten-thousands  and  how  many  thousands 
over?  Write  4  thousands  in  thousands'  place  and  2  ten- 
thousands  in  ten-thousands'  place  in*  the  product. 

The  work  may  be  expressed  thus : 

4127  Multiplicand, 
x  6  Multiplier. 


24762  Product. 


108  PRIMARY   ARITHMETIC 

58.   Written. 

Find  the  products : 


1. 

45 
5 

2.   36 

4 

3.   82 

7 

4.    63 

6 

5. 

72 
9 

6.    84 
5 

7.   43 

9 

8.    35 

8 

9. 

75 
6 

10.   98 

9 

11.   73 
10 

12.    68 
11 

13. 

$123 
9 

14.   $236 
5 

is.   $384 

8 

16.   $721 
9 

17. 

1398 
10 

18.   $4.32 
5 

19.   $2.36 
8 

20.   $3.95 
4 

21. 

387 
12 

22.   792 

7 

23.    684 
4 

24.     199 

12 

25. 

1306 
5 

26.    2908 
9 

27.   4908 
6 

28.    3967 

7 

29. 

3872 
8 

so.    3963 
11 

31.    5984 

7 

32.   7983 
10 

33. 

3161 
11 

34.   5184 

9 

35.    3872 
5 

36.   4560 

8 

Mu 

Itiply  these 

numbers  by 

2,  5,  6,  9,  8,  7: 

37.  42,608          39.   29,132          41.   18,736          43.   32,984 

38.  36,975          40.   13,671          42.   28,416          44.   15,116 


MULTIPLICATION  109 

59.   1.   Write  536.    In  what  place  is  the  6  ?    The  3?  The  5? 

Annex  a  cipher  to  536.     Thus,  5360. 

In  5360,  what  places  do  the  6,  3,  and  5  occupy  ?  What 
has  been  done  to  each  figure  ? 

Moving  a  figure  one  place  to  the  left  affects  its  value  how  ? 
(See  principles  of  Arabic  notation.)  Since  the  value  of  each 
figure  has  been  multiplied  by  10,  what  has  been  done  to  the 
entire  number  ? 

Since  annexing  a  cipher  to  a  number  multiplies  it  by  10, 
what  would  you  do  to  multiply  a  number  by  ten  ? 

2.  Multiply  these  numbers  by  10  : 

25,  342,  607,  4936,  8972, -400,  91. 

How  can  you  multiply  a  number  by  100  ?  By  1000  ? 
By  10000  ? 

3.  Multiply  the  following  numbers  by  100,  1000,  10000  : 

29,  341,  256,  9203,  4216,  899. 

4.  Multiply  876  by  80. 

80  =  8  x  10.     876  x  80  =  876  x  8  x  10 
First  multiply  876  by  8,  then  by  10,  thus : 

876 

80     How  did  we  multiply  by  10  ? 
70080     Product. 

5.  Multiply  876  by  800. 

800  =  8  x  100.     876  x  800  =  876  x  8  x  100,  thus : 

876 

800     How  did  we  multiply  by  100  ? 
700800     Product. 

How  could  you  multiply  by  7000? 

6.  Multiply  1283  by  967. 

967  =  900  +  60  +  7. 


110  PRIMARY   ARITHMETIC 

Multiply  1283  by  7,  by  60,  by  900,  and  add  the  three  products,  thus : 

1283 

967 

8981 

76980 

1154700 


1,240,661     Product. 

The  ciphers  at  the  right  of  the  partial  products  may  be  omitted,  thus : 

1283 
967 
8981 
7698 
11547 
1,240,661     Product. 

60.    From  the  above  examples  we  may  make  the  following 


Rule  for  Multiplication 

1.  Write  the  multiplier  under  the  multiplicand. 

2.  Multiply  the  units   in  the  multiplicand    by  the 
multiplier.     If  this  product  is  less  than  10,  write  it  in 
units'  place  in  the  product.     If  10  or  greater  than  10, 
divide  it  by  10  and  write  the  remainder  in  units'  place 
in  the  product,  adding  the  quotient  to  the  product  of 
the  tens.     Proceed  in  a  similar  way  toward  the  left  till 
all  the  figures  of  the  multiplicand  have  been  multiplied. 

3.  If  the  multiplier  contains  more  than  one  figure, 
multiply  the  multiplicand  by  each  figure  of  the  multi- 
plier separately,  writing  the  first  figure  of  each  partial 
product  under  the  figure  multiplied  by,  and  add  the 
partial  products. 

4.  In  multiplying  Federal  money  put  the   decimal 
point  in  the  product  under  the  decimal  point  in  the 
multiplicand. 


MULTIPLICATION  111 

61.  Multiply 

1.  324  x  24  12.  598  x  36  23.  $36.915  x  45 

2.  296  x  39  13.  287  x  49  24.  $126.93  x  87 

3.  387  x  45  14.  799  x  99  25.  $17.856  x  48 

4.  263  x  56  is.  296  x  28  26.  $19.634  x  49 

5.  892x63  is.  694x39  27.  $75.105x97 

6.  728  x  75  17.  206  x  54  28.  $16.351  x  64 

7.  398  x  84  is.  $28.15  x  28  29.  $280.52  x  36 

8.  987  x  98  19.  $34.98  x  27  30.  $356.04  x  28 

9.  516  x  31  20.  $19.845  x  46  31.  $987.62  x  75 

10.  798  x  43  21.   $7.852  x  124         32.   $396.41  x  41 

11.  896x79  22.   $28.754x15         33.   $806.04x79 

62.  i.    31  x  10  x  200  =  ? 

2.  A  has  172  sheep,  and  B  3  times  as  many.     How  many 
has  B? 

3.  There  are  56  pounds  in  one   bushel  of   salt.     How 
much  will  7  bushels  weigh  ? 

4.  What  will  6  acres  of  land  cost,  at  $84  an  acre  ? 

5.  Find  the  cost  of  8  bushels  of  potatoes  at  $  .45  a  bushel. 

6.  There  are  320  rods  in  1  mile.     How  many  rods  in  9 
miles  ? 

7.  How  many  yards  in  5  miles,  there  being  1760  yards 
in  one  mile  ? 

8.  At  $1.75  a  bushel,  what  will  10  bushels  of  walnuts 
cost  ? 

9.  If  a  train  travels  at  the  rate  of  53  miles  an  hour,  how 
far  will  it  travel  in  11  hours  ? 

10.    In  an  orchard  there  are  32  peach  trees  in  a  row,  and 
12  rows.     How  many  trees  in  the  orchard  ? 


112  PRIMARY   ARITHMETIC 

11.  At  $2.50  a  day,  what  will  a  man  earn  in  6  days  ? 

12.  Find  the  cost  of  9  yards  of  silk  at  $2.15  a  yard. 

13.  How  many  pounds  in  4  barrels  of  flour,  there  being 
196  pounds  in  one  barrel  ? 

14.  If  1  sack  of  flour  is  worth  $1.35,  what  must  be  paid 
for  6  sacks  of  flour  ? 

15.  At  $5.25  a  ton,  what  will  12  tons  of  coal  cost  ? 

16.  Find  the  cost  of  10  tons  of  hay  at  $10.50  a  ton. 

17.  There  are  5280  feet  in  1  mile.     How  many  feet  are 
there  in  7  miles  ? 

18.  There    are    2000    pounds    in    one   ton.      How   many 
pounds  are  there  in  10  tons  ? 

19.  If  it  costs  $384  to  pay  the  hands  in  a  certain  factory 
for  one  day,  what  will  be  the  amount  of  the  weekly  pay- 
roll ? 

20.  What  must  be  paid  for  86  quarts  of  berries  at  12  cents 
a  quart  ? 

21.  The  yearly  expenses  of  a  certain  family  are  $642. 
What  are  the  expenses  of  a  family  using  3  times  as  much  ? 

22.  If  the  average  daily  attendance  at  a  certain  school  is 
563,  what  is  the  attendance  for  10  days  ? 

23.  Mr.  Smith  has  174  acres  of  land,  and  his  neighbor  5 
times  as  much.     How  many  acres  has  his  neighbor  ? 

24.  If  a  cord   of  wood  costs  $4.50,  what  will  11   cords 
cost  ? 

25.  There  are  144  pens  in  1  gross.     How  many  pens  are 
there  in  12  gross  ? 

26.  How  many  pounds  in  8  barrels  of  sugar,  if  each  barrel 
weighs  327  pounds  ? 


DIVISION 


63.  Division  is  the  process  of  finding  how  many  times  one 
number  is  contained  in  another,  or  finding  one  of  the  equal 
parts  of  a  number.     Thus,  5  cents  is  contained  in  20  cents 
4  times.     One-fourth  of  20  cents  is  five  cents. 

64.  The  number  divided  is  the  Dividend.     The  number  by 
which  another  number  is  divided  is  the  Divisor. 

65.  The  result  of  division  is  the  Quotient. 

dividend  divisor          quotient 

Thus,  45  divided  by  9      =       5. 

The  dividend,  divisor,  and  quotient  are  called  the  Terms 
of  Division. 

66.  When   the  divisor  is  not   exactly  contained    in  the 
dividend,  the  part  of  the  dividend  that  is  left  is  called  the 
remainder.     Thus,  59  divided  by  8  =  7  and  3  remainder. 

67.  The  Sign  of  Division  is  a  short  horizontal  line  with  a 
dot  above  and  a  dot  below  it.      When  placed  between  two 
numbers,  it  shows  that  the  first  is  to  be  divided  by  the 
second.     Thus,  80  -*•  10  =  8. 

68.  Division  is  also  indicated  by  placing   the  dividend 
above  and  the   divisor  below  a  horizontal  line.     Thus,  -^ 
means  12  -5-  3 ;   or  ^   means  1  -s-  3,  or  1  whole  thing  divided 
into  3  equal  parts. 

113 


114  PRIMARY   ARITHMETIC 

69.  Tell  quotients  at  sight : 

4  x   ?  =    8                     2  in  14=?  ?  x    2  =  12 

6  x   ?  =18                     4  in  48=  ?  ?  x    5  =  45 

7x   ?  =28                   12in84=?  ?  x    6  =  30 

4  x   ?  =  36                      6  in  36  =  ?  ?  x    4  =  36 

2  x   ?  =  24                      9  in  45  =  ?  ?  x    8  =  40 

3  x   ?  =  33                     4  in  44  =  ?  ?  x    7  =  63 

6  x   ?  =  24                    12  in  60  =?  ?  x  12  =  48 

7  x   ?  =  56                      9  in  36  =?  ?  x    8  =  32 

4  x   ?  =  36                      8  in  64  =  ?  ?  x    9  =  81 

120-12=?  99-9=?  120-10=? 

100-10=?  66-11=?  80-8=? 

90  -    9  =  ?                      44  -    4  =  ?  108  -    9  =  ? 

80  -  10  =  ?                   '  54  -    9  =  ?  48  -    4  =  ? 

48  -    8  =  ?                      84  -  12  =  ?  90  -  10  =  ? 

63  -    7  =  ?                     50  -    5  =  ?  72  -  12  =  ? 

81-9=?                      54-6=?  49-7=? 

72-6=?                      24-8=?  25-5=? 

28-7=?                      24-2=?  64-8=? 

35  -  7.=  ?  40  -  4  =  ?  60  -  5  =  ? 

132-11=?  22-11=?  63-7=? 

108  -  12  =?  32  -  8  =  ?  84  -  7  =  ? 

70.  Oral. 

1.  At  12  cents  each,  how  many  books  can  be  purchased 
for  72  cents  ? 

2.  How  many  dozen  in  84  oranges  ? 

3.  When  8  pounds  of  sugar  cost  40  cents,  what  is  the 
price  of  a  pound  ? 

4.  Among  how  many  boys  can  45  cents  be  divided  if 
each  boy  receives  9  cents  ? 

5.  There  are  108  pencils  in  108  equal  packages.     How 
many  pencils  in  each  package  ? 


LONG  DIVISION  115 

6.  If  6  tons  of  hay  cost  72  dollars,  what  will  1  ton  cost  ? 

7.  When  milk  is  5  cents  a  quart,  how  many  quarts  can 
be  purchased  for  40  cents  ? 

8.  Paid  $55  for  11  tons  of  coal.     What  was  the  price  of 
1  ton? 

9.  There  are  48  pecks  of  corn  in  a  bin.     There  being  8 
pecks  in  a  bushel,  how  many  bushels  in  a  bin  ? 

10.  There  are  8  pints  in  a  gallon.     How  many  gallons  in 
96  pints  of  vinegar  ?    . 

11.  A  dime  is  ten  cents,  and  there  are  10  dimes  in  a  dollar. 
How  many  dollars  are  there  in  80  dimes  ? 

12.  A  laborer  earns  56  dollars  in  7  weeks.     How  much 
does  he  earn  in  1  week  ? 

13.  If  11  boxes  of  berries  sell  for  77  cents,  what  is  the 
price  of  1  box  ? 

14.  I  pay  77  cents  for  berries  at  7  cents  a  box.      How 
many  boxes  do  I  purchase  ? 

15.  Bought  9  yards  of  cloth  for  108  cents.     How  much 
did  I  pay  for  1  yard  ? 

16.  At  12  cents  a  yard,  how  many  yards  of  cloth  can  be  • 
bought  for  108  cents  ? 

17.  A  boy  wishes  to  buy  a  bicycle  that  costs  60  dollars. 
In  how  many  weeks  can  he  earn  money  enough  to  pay  for  it 
at  $5  a  week? 

LONG  DIVISION 

71.   l.    Divide  4932  by  9. 

Write  the  divisor  at  the  left  of  the  dividend  with  a  line  014939 
between,  thus : 

How  many  thousands  times  is  9  contained  in  4  thousands?  (No 
thousand  times.)  4  thousand  9  hundred  make  how  many  hundreds? 
How  many  hundreds  times  is  9  contained  in  49  hundreds? 


116 


PRIMARY  ARITHMETIC 


Write  5  hundreds  in  the  hundreds'  place  in  the 
quotient,  thus : 

5  hundred  times  9  'are  how  many  hundreds? 
Write  45  hundreds  under  49  hundreds  and  subtract, 
thus : 

How  many  hundreds  over  ? 

Bring  down  three  tens  from  the  dividend,  thus : 
4  hundreds  and  3  tens  make  how  many  tens? 
How  many  tens  times  is  9  contained  in  43  tens? 


Write  4  tens  in  the  quotient,  thus : 


4  tens  times  9  are  how  many  tens?     Write  36 
tens  under  43  tens  and  subtract,  thus : 
How  many  tens  over  ? 


Bring  down  2  units  from  the  dividend,  thus : 


5  Quotient. 
9 1 4932  Dividend. 

5 Quotient. 

9 1 4932  Dividend. 

45 

4 

5 Quotient. 

9 1 4932  Dividend. 
45 

43 

54  Quotient. 
9)4932  Dividend. 
45 

43 

54  Quotient. 
9 1 4932  Dividend. 

!5_ 
43 

36 

7 

54     Quotient. 
9 1 4932  Dividend. 
45 
43 
36 
72 

548  Quotient. 
9 1 4932  Dividend. 
45 
43 
36 
72. 
72 


How  many  times  will  72  units  contain  9  ?  Write 
8  in  units'  place  in  the  quotient;  multiply  9  by  8 
and  write  the  product  under  72,  thus : 

Subtract.  How  many  over?  What  is  the  quo- 
tient? 

2.    Divide  3553  by  17. 

209  Quotient 

17 1  3553  Dividend  In  this  example,  17  is  not  contained   any  tens 

34  times  in  15  tens ;  so  we  put  0  in  tens'  place  in  the 

153  quotient  and  bring  down  3  units. 

153 


LONG  DIVISION  117 

3.   Divide  835,176  by  672. 

1242  Quotient  +  552  Remainder. 
672  1  835176  Dividend. 
672 

In  this  example,  the  dividend  does  not  contain 
the  divisor  an  exact  number  of  times,  hence  there 
9^00  is  a   remainder.      This  remainder  may  be  written 

over    the    divisor    as    part    of    the    quotient    thus: 


1344 
552  Rem. 

72.    From  the  foregoing  examples,  we  may  make  the  fol- 
lowing 


Rules  for  Long  Division 

1.  Write  the  dividend  at  the  right  of  the  divisor 
with  a  line  between. 

2.  Beginning  at  the  left,  find  how  many  figures  of 
the    dividend    are    necessary  to    contain    the    divisor. 
Divide  the  number  represented  by  these  figures  by  the 
divisor,  and  write  the  quotient  above  the  last  figure 
of  the  dividend  used. 

3.  Multiply  the  divisor  by  the  quotient  just  obtained, 
and  subtract  that  product  from  the  partial  dividend  used. 

4.  Annex  to  the  remainder  the  next   figure  of  the 
dividend,  and   use   the   number   obtained   as  the  next 
partial  dividend.     Proceed  as  before  and  continue  the 
process  until  all  the  figures  of  the  dividend  have  been 
used. 

5.  In  dividing  Federal  money,  put  the  decimal  point 
in  the  quotient  the  same  number  of  places  from  the 
right-hand  side  as  is  the  decimal  point  in  the  dividend. 


118  PRIMARY  ARITHMETIC 

73.  Find  the  quotients  : 

1.  392-14  is.    5436-18  28.      1289-73 

2.  1124-18  16.    1286-39  29.    16,428-84 

3.  3726 -h  24  17.    2983-42  so.    12,582-58 

4.  485-17  is.  1008-25  31.  1384-75 

5.  793-15  19.  9436-^47  32.  6381-5-86 

6.  851-27  20.  8059-36  33.  12,946-5-24 

7.  507-^-16  21.  1583-46  34.  9273-91 

8.  943-22  22.  4109-51  35.  7754-78 

9.  1240-21       23.  2695-57      36.  10,846-^45 

10.  1296^13  24.  3874-49  37.  21,431-36 

11.  1364-19  25.  9003-25  38.  27,473-97 

12.  3964-32  26.  5914-59  39.  35,702-53 

13.  1289-16  27,  5630-62  40.  40,060-60 

14.  5683-37 

SHORT   DIVISION 

74.  When  the  divisor  is  a  small  number,  the  work  of  divi- 
sion  may  be   shortened  by  omitting  all  the  figures  except 
those   of  the   dividend,  divisor,  and  quotient,  and  writing 
the  quotient  under,  instead  of  over,  the  dividend.     By  this 
method,  all  the  processes  are  performed,  just  as  in  long  divi- 
sion, but  are  not  written. 

EXAMPLES 
1.    Divide  347,615  by  5. 

51347615  Dividend. 


69523  Quotient. 


SHORT  DIVISION  119 

2.    Divide  20,076  by  12. 

12  1  20076    Dividend. 
1673    Quotient. 

Every  division  by  numbers  not  larger  than  12  should  be 
performed  by  short  division. 

75.   Written.     Find  the  quotients-: 

1.  2555-5  19.      30,005-*-    5          37.     31,493-    6 

2.  2436  +•  4  20.   288,012-12          38.      25,324-    5 

3.  2845  -r-  5  21.    300,010  -  10          39.      28,764  -    4 

36,099  -  9 
14,412-12 
36,930  -  11 
24,003-  6 
30,502  -  8 
29,333  -  11 

46.  675,262-  5 
,872-  8 

48.    130,052-    2 

13.  H|JL8.  31.      82,956-10          49.   168,754-    9 

14.  iAjMJ.  32.     93,043-    7          so.    385,980-    5 
is.   jLLjpi                33.     65,407-    5         51.   769,520-    7 

16.  JUL|iMi  34.      39,842-    9         52.    387,052-10 

17.  2Ji|jy>  35.     27,391-    8         53.   943J69  -  12 

18.  M|Afi.  36.      63,598  -    9         54.    748,131  -    4 


4. 

4503-f- 

3 

22. 

99,011  - 

11 

40. 

5. 

2045- 

5 

23. 

33,264- 

11 

41. 

6. 

2835- 

7 

24. 

29,280  - 

12 

42. 

7. 

4986- 

9 

25. 

36,550  - 

10 

43. 

8. 

2009- 

7 

26. 

28,692  - 

9 

44. 

9. 

3504  - 

8 

27. 

333,333  - 

11 

45. 

10. 

H1|JL8 

28. 

35,621  - 

7 

46. 

11. 

2_8|4_3 

29. 

42,963  ^ 

6 

47. 

12. 

£.98.10 

30. 

50,725  - 

3 

48. 

120  PRIMARY   ARITHMETIC 

SPECIAL  CASES   IN  DIVISION 

76.    Any  number,  as  34,765,  may  be  analyzed  as  follows: 
34,765  =  34,765  units;  or,  3476  tens  and  6  over;  or,  347 

hundreds  and  65  over  ;  or,  34  thousands  and  765  over  ;  or, 

3  ten  thousands  and  4765  over.     Therefore, 


34,765  +  10         =  3476^       or 

T 

I9^ 

Quotient. 


3476T%  Quotient. 
34,765  +  100       =  347^       or     I9^ 


34,765+1000     =34T^        or 

Quotient. 


34,765  +20         =  Juyu  +  ^  or 


j5o  Quotient. 

O  4     *7  f*  C  f  A  A  Q  A  *7  R  K.  *J\JyJ   )  OT:  I  yJfJ 

•34,765  -T-  500       =  5A1  +  65   or       r  ; 

69|^-|  Quotient. 

77.    Hence  the 


Rule  for  Special  Cases  in  Division 

1.  To  divide  by  1  with  any  number  of  ciphers  an- 
nexed, cut  off  from  the  right-hand  side  of  the  dividend 
as  many  figures  as  there  are  ciphers  in  the   divisor. 
The  figures  cut  off  will  express  the  remainder,  and  the 
figures  not  cut  off  will  be  the  quotient. 

2.  To  divide  by  any  number  ending  in  one  or  more 
ciphers,  cut  off  from  the  right-hand  side  of  the  dividend 
as  many  figures  as  there  are  ciphers  at  the  right  side  of 
the  divisor.     Cut  off  the  ciphers  from  the  right  of  the 
divisor.     Divide  the  part  of  the  dividend  left  by  the 
part  of  the  divisor  left,  and  prefix  the  remainder  ob- 
tained, if  any,  to  the  figures  cut  off,  for  a  remainder  to 
the  entire  division. 


DIVISION  121 

78.    Find  the  quotients: 


1. 

1|OQ)369|QO 
369 

2.  1|QO)283|25 

3. 

1|000)36|954 

4. 

35,800 

-r-10 

10. 

36,900 

-100 

16. 

253,000 

-1000 

5. 

78,563 

-flO 

11. 

85,982 

-100 

17. 

287,604 

-*-1000 

6. 

50,625 

+  10 

12. 

36,984 

+  100 

18. 

129,832 

-r-1000 

7. 

36,072 

+  10 

13. 

28,305 

-100 

19. 

172,001 

^1000 

8. 

25,600 

+  10 

14. 

72,601 

-f-100 

20. 

398,436 

+  1000 

9. 

35,690 

-10 

15. 

35,100 

-i-100 

21. 

128,000 

+  1000 

22. 

136,948 

-50 

23.   169,846 

-80 

24. 

389,063 

-*• 

200 

25.  8,698,751-500 

79.  l.    24  —  ?  =  8.     Which  terms  of  division  are  given  ? 
To  find  what  ?     How  do  you  find  it  ?     When  the  dividend 
and  quotient  are  given,  how  can  the  divisor  be  found  ? 

2.  ?  —  3  =  8.  Which  terms  are  given  ?  To  find  what  ? 
How  do  you  find  it  ?  When  the  divisor  and  quotient  are 
given,  how  may  the  dividend  be  found  ?  State  two  ways. 

80.  These  examples  show  the  following 


Proof  of  Division 

1.  Divide    the    dividend   by   the   quotient.     If   the 
result  is  the  same  as  the  divisor,  the  work  is  correct. 
The  remainder,  if  any,  should  be  the  same  as  in  the 
first  division. 

2.  Multiply  the  quotient  and  divisor  together.    Add 
the  remainder,  if  there  is  any,  to  the  product.     If  the 
result  obtained  is  the  same  as  the  dividend,  the  division 
is  correct. 


122  PRIMARY   ARITHMETIC 

81.  1.    9  x  2  =  ?     Which  term  is  9  ?     Which  term  is  2  ? 
2x9  =  ?     Which  term  is  9  ?     Which  term  is  2  ? 
Compare  the  results  in  the  above  examples. 

2.  ?  x  2  =  18.  Which  terms  are  given  ?  Which  term 
to  find  ?  How  do  you  find  it  ?  When  the  multiplier  and 
product  are  given,  how  can  the  multiplicand  be  found  ? 

9  x  ?  =  18.  When  the  product  and  multiplicand  are  given, 
how  can  the  multiplier  be  found  ? 

82.  These  examples  show  the  following 


Proof  of  Multiplication 

1.  Multiply  the  multiplier  by  the  multiplicand.     If 
the  work  is  correct,  the  product  obtained  will  agree 
with  the  first  product.     Or, 

2.  Divide   the    product  by  the  multiplier.     If   the 
work  is  correct,  the  quotient  will  be  the  same  as  the 
multiplicand.      Or, 

3.  Divide  the  product  by  the  multiplicand.     If  the 
work  is  correct,  the  quotient  will  be  the  same  as  the 
multiplier. 


PROBLEMS   IN  DIVISION 
83.   Written. 

1.  If  a  steamboat  ran  1440  miles  in  4  days,  what  was  the 
average  rate  for  a  day? 

2.  A  farmer  put  1068  bushels  of  potatoes  in  6  bins.     How 
many  bushels  were  in  each  bin  ? 

3.  A  girl  divided  $4.50  among  10  poor  children.     How 
much  did  she  give  to  each? 


PROBLEMS   IN   DIVISION  123 

4.  How  many  tons  of-  coal  at  $  5  a  ton  can  be  bought  for 

$765? 

5.  If  7  men  can  build  378  rods  of  fence  in  a  week,  how 
many  rods  can  one  man  build  in  the  same  time  ? 

6.  How  many  days,  at  11  miles  a  day,  will  it  take  a  man 
to  walk  902  miles  ? 

7.  The  dividend  is   981,  the  quotient  9.     What  is  the 
divisor? 

8.  How  many  ploughs  at  1 12  each  can  be  bought , for 

$1008? 

9.  A  man  divided  2222  acres  of  land  into  11  parts.     How 
many  acres  were  there  in  each  part  ? ' 

10.  A  farmer  paid  $46.25  for  10   sheep.     What  did  he 
pay  for  each? 

11.  There  are  8  quarts  in  1  peck.     How  many  pecks  are 
there  in  3320  quarts? 

12.  There  are  7  days  in  1  week.      How  many  weeks  in 
364  days? 

13.  A  man  willed  $19,722  to  his  6  children.     How  much 
did  each  receive,  if  they  shared  equally  ? 

14.  What  is  the  price  of  1  yard  of  broadcloth,  if  12  yards 
cost  $50.40? 

15.  There  are  5280  feet  in  a  mile,  and  3  feet  in  1  yard. 
How  many  yards  in  a  mile? 

16.  At  $  8  each,  how  many  overcoats  can  be  bought  for 


17.  How  many  hours  will  be   required  to  ride  a  bicycle 
504  miles  by  riding  18  miles  an  hour? 

18.  At  $  15  each,  how  many  suits  of  clothes  can  be  bought 
for  $1080? 


124  PRIMARY   ARITHMETIC 

19.  If  a  family  consume  13  gallons  of  kerosene  in  a  month, 
in  how  many  months  will  it  consume  468  gallons? 

20.  At  $16  a  ton,  how  many  tons  of  hay  can  be  bought 
for  $1920? 

21.  If  1   acre  of  land  yiejds  24  bushels  of  wheat,  how 
many  will  be  required  to  yield  2544  bushels  ? 

22.  At  $27  each,  how  many  stoves   can  be  bought  for 
$648? 

23.  If  a  man  can  walk  30  miles  in  1  day,  in  how  many 
days  can  he  walk  1000  miles? 

24.  How  many  weeks  will  it  take  to  pay  a  debt  of  $  1225 
by  paying  $  25  a  week  ? 

REVIEW   EXERCISES 

84.    Oral. 

1.  A  farmer  sold  12  barrels  of  apples  at  $3  a  barrel  and 
bought  with  the  proceeds  coal  at  $4  a  ton.     How  many  tons 
did  he  buy  ? 

2.  A  .dealer  bought  10  barrels  of  apples  at  $  2  a  barrel  and 
sold  them  so  as  to  gain  $10.     What  was  the  selling  price 
per  barrel  ? 

3.  In  what  time  will  a  boy  at  $  3  a  week  earn  as  much  as 
a  man  earns  in  4  weeks  at  $9  a  week? 

4.  John  had  $  6,  James  3  times  as  much,  and  Thomas  J  as 
much  as  both.     How  much  had  Thomas  ? 

5.  A  man  who  carried  56  eggs  to  market  found  -|  of  them 
broken.     How  many  were  not  broken  ? 

6.  Nell  is  three  years  old,  and  Will  5.     Their  sister  is  as 
old  as  twice  the  sum  of  their  ages.     How  old  is  their  sister  ? 

7.  A  farmer  sold  48  pecks  of  beans  for  $48.     How  much 
did  he  receive  a  bushel,  there  being  4  pecks  in  a  bushel  ? 


REVIEW   PROBLEMS  125 

8.  Bought  a  dozen  oranges  for  36  cents  and  sold  them  at 
4  cents  apiece.      What  was  the  entire  profit  ? 

9.  How  many  gallons  of  milk  will  a  family  use  in  12  days 
if  they  use  2  quarts  a  day,  there  being  4  quarts  in  a  gallon  ? 

10.  Mr.  A  owed  a  debt  of  $96.     He  made  5  payments  of 
$  12  each.     How  much  remained  unpaid  ? 

11.  Two  boys  80  miles  apart  travel  toward  each  other. 
The  first  goes  5  miles  an  hour,  and  the  second  3  miles  an 
hour.     In  how  many  hours  will  they  meet  ? 

12.  Two  boys,  travelling  at   the  rate  of   5  miles   and   3 
miles  an  hour  respectively,  go  in  the  same  direction.     How 
far  apart  are  they  at  the  end  of  6  hours  ? 

13.  If  I  can  buy  7  oranges  for  14  cents,  how  many  can  I 
buy  for  24  cents? 

14.  By  selling  12  barrels  of  flour  at  $5  a  barrel,  a  grocer 
makes  a  profit  of  $12.     What  was  the  cost  of  the  flour  per 
barrel ? 

REVIEW   PROBLEMS 

85.   Written. 

1.  If    the    dividend   is    1821,  the  quotient    32,  and  the 
remainder  29,  what  is  the  divisor  ? 

2.  The  product  of  three  numbers  is  1260,  and  two  of 
them  are  12  and  7.     What  is  the  third? 

3.  A  grocer  buys  88  gallons  of  molasses  at  $.56  a  gallon. 
For  how  much  per  gallon  must  he  sell  it  in  order  to  gain 
$12.32? 

4.  Two  railway  trains  start  at  the  same  time  from  oppo- 
site points,  1216  miles  apart,  and  travel  toward  each  other, 
one  going  35  miles  an  hour,  and  the  other  41  miles  an  hour, 
How  many  hours  before  they  will  meet  ? 


126  PRIMARY   ARITHMETIC 

5.  Two  steamboats  are  144  miles  apart  and  going  in  the 
same  direction,  one  at  the  rate  of  21  miles,  and  the  other  15 
miles,  an  hour.     In  how  many  hours  will  the  former  over- 
take the  latter  ? 

6.  A  merchant  bought  8  pieces  of  cloth,  each  containing 
52  yards,   at  12   cents  a  yard,  and  325  pounds  of    cotton 
batting  at  9  cents  a  pound.     How  much  less  than  $100  did 
it  cost  him  ? 

7.  If  64  pounds  of  butter  costs  $15.36,  what  will  320 
pounds  cost  at  the  same  price  ? 

8.  A  grocer  bought  123  gallons  of  molasses  at  42  cents 
a  gallon  and  sold  it  at  60  cents  a  gallon.      What  was  his 
gain  ? 

9.  A  man  bought  4   cows  at  one  time  for  $168,   3  at 
another  for  $153,  and  6  at  another  for  $225.     What  was 
the  average  price  paid  ? 

10.  Divide  the  product  of  27  and  32  by  their  sum. 

11.  If  18  men  can  build  a  wall  in  120  days,  in  what  time 
can  24  men  build  it  ? 

12.  A  man,   dying,  left  property  amounting   to   $3500. 
After   paying   $  572    for   funeral    and    other    expenses,    the 
remainder  was  divided  equally  among  12  heirs.     What  did 
each  receive  ? 

13.  Two  vessels  start  from   the   same  point  and  sail  in 
opposite  directions,  one  at  the  rate  of  18   miles,   and   the 
other  23  miles,  an  hour.     How  far  apart  will  they  be  in  16 
hours  ? 

14.  I  bought  124  bushels  of  corn  of  A,  216  of  B,  and  96 
of  C,  paying  $.63  a  bushel  in  each  case.      What  will  be  my 
profit  if  I  sell  the  whole  at  $.72  a  bushel  ? 


REVIEW   PROBLEMS  127 

15.  A  man  starts  on  a  journey  of  724  miles.     When  he 
has  travelled  12  hours  at  the  rate  of  32  miles  an  hour,  how 
far  is  he  from  his  journey's  end  ? 

16.  A  man  bought  6  sacks  of  flour  at  $1.25  a  sack,  24 
pounds  of  sugar  at  6  cents  a  pound,  and  2  pounds  of  coffee 
at  35  cents  a  pound,  and  paid  for  it  in  butter  at  23  cents  a 
pound.     How  many  pounds  were  there  ? 

17.  If  I  sell   58  cows  at  $38  a  head,  and  200  sheep  at 
$4.30  a  head,   and  invest   the  proceeds   in  4  village   lots, 
what  is  the  average  price  of  each  lot  ? 

18.  I  bought  a  city  lot  for  $1750,  built  a  house  upon  it  at 
a  cost  of  $3275,  and  afterward  sold  the   place  for  $6000. 
What  was  my  gain  ? 

19.  A  boy  has  $9.62  in  his  toy  bank.     How  many  times 
can  he  take  away  25  cents  from  it,  and  have  12  cents  left  ? 

20.  A  man  bought  a  house  and  lot  for  $3200.     He  paid 
$1275  down,  and   agreed   to   pay  the  remainder   in   equal 
monthly  payments  of  $35  each.     How  many  months  will  it 
take  to  pay  in  full  ? 

21.  The   product  of  four  numbers  is  2880,  and  three  of 
them  are  5,  6,  and  8.     What  is  the  fourth  ? 

22.  A  teacher  who  receives   a   monthly  salary  of   $125 
for  10  months  in  a  year  will   require   how  many  years  to 
pay  for  3  village  lots  at  $645  each,  if  his  yearly  expenses 
are  $863? 

23.  A  man  having  $783.58  in  bank,  drew  out  $132.75  at 
one  time,  $175.50  at  another,  $216  at  another.     How  much 
then  remained  in  the  bank  ? 

24.  How  many  tons  of  coal  at  $5  a  ton  will  pay  for  15 
tons  of  hay  at  $11  a  ton? 


128  PRIMARY   ARITHMETIC 

25.  If  a  pupil  in  school  uses  6  sheets  of  writing  paper 
each  day,   how  many  tablets  containing  75  sheets  will  he 
require  for  the  school  year  of  40  weeks  of  5  days  each,  if  he 
attends  school  every  day,  making  no  allowance  for  holidays? 

26.  I  paid  $365  for  a  horse  and  carriage,  paying  $1  more 
for  the  horse  than  for  the  carriage.     What  did  I  pay  for 
each  ? 

27.  A  farmer  paid  $1125  for  cows,  horses,  and  farming 
tools,  and  8  times  as  much  for  a  farm  of  125  acres.     What 
was  the  price  p^r  acre  ? 

28.  John,    Edward,    and    Henry   have    together   $12.80. 
John  has  $2. 26  more  than   Henry,  and   Edward  has  $1.75 
more  than  Henry.     How  much  money  has  each  ? 

29.  A  man  bought  84  acres  of  land  at  $65  an  acre  and 
sold  it  all  for  $  6552.     What  was  his  gain  per  acre  ? 

30.  A  merchant  bought  172  yards  of  cashmere  at  $.45  a 
yard,  504  yards  of  calico  at  $.05,  252  yards  of  flannel  at 
$ .  37,  and  paid  for  it  in  3  equal  payments.     What  was  the 
amount  of  each  payment  ? 

31.  A  drover  bought  27  COWTS  for  $1026.     At  what  price 
per  head  must  he  sell  them  to  make  a  profit  of  $12  on  each  ? 

32.  There  are  24  sheets  of  paper  in  a  quire.     How  many 
sheets  in  2  reams,  there  being  20  quires  in  a  ream  ? 

33.  A  man  bought  1000  sheep  and  sold  at  one  time  216, 
at  another  327,  and  at  another  198.     How  many  did  he  then 
have  left? 

34.  There  are  640  acres  in  1  square  mile.     Into  how  many 
farms  of   160  acres   each   can  10   square   miles   of   land  be 
divided  ? 

35.  A  merchant  bought  dress  goods  at  $1.26  a  yard  and 
sold  it  at  $2  a  yard.      What  was  his  profit  on  260  yards  ? 


REVIEW   PROBLEMS  129 

36.  I  sold  a  farm  for  $  1265  more  than  I  paid  for  it,  but 
$  325  less  than  my  asking  price.     What  would  have  been 
my  profit  if  I  had  sold  at  my  asking  price  ? 

37.  How  many  more  acres  of  land  can  I  buy  with  $  6048 
at  $56  an  acre  than  at  $  72  an  acre  ? 

38.  A  grocer  bought  123  pounds  of  cheese  at  10  cents  a 
pound  and  sold  it  for  13   cents  a  pound.     What  was  his 
profit  ? 

39.  A  lady  bought  12  yards  of  dress  goods  at  $  1.75  a 
yard,  8  yards  of  silesia  at  $.25  a  yard,  2  pairs  of  gloves  at 
$1.45  a  pair,  6  handkerchiefs  at  $.25  apiece,  and  3  yards 
of  table  linen  at  $.95  a  yard.     She  pai'd  $18.75  and  left  the 
balance  on  account.     What  did  she  still  owe  ? 

40.  How  many  pounds  of   butter  at  26    cents   a  pound 
must  be  given  for  3  barrels  of  flour  at  $4.20  a  barrel? 

41.  At  what  rate  per  hour  must  a  railway  train  run  to 
overtake,  in  12  hours,  another  train  168  miles  ahead  running 
at  the  rate  of  32  miles  an  hour? 

42.  How  many  more  revolutions  will  a  wheel  10  feet  in 
circumference  make  in  going  5280  feet,  or  a  mile,  than  one 
20  feet  in  circumference  ? 

43.  How  much  more  will  8  horses  at  $  165  each  cost  than 
23  cows  at  $  37  a  head  ? 

44.  From  a  bin   containing    324   bushels    of   wheat,   147 
bushels  were    sold   at   $  .85,  and  the    remainder   at   $.90  a 
bushel.     What  did  the  wheat  bring? 

45.  A  man  buys  32  cows  for  $1120  and  sells  them  at  a 
gain  of  $192.     What  does  he  receive  a  head  for  them  ? 

46.  How  many  hours  will  it  take  a  horse,  travelling  8 
miles  an  hour,  to  go  as  far  as  a  train  of  cars  can  go  in  4 
hours  running  at  the  rate  of  35  miles  an  hour  ? 


FACTORING 


86.  A  number  that  will  divide  another  number  without 
a  remainder  is  an  Exact  Divisor  of  that  number. 

87.  An  exact  divisor  of  a  number  is  a  Factor  of  that  num- 
ber.    Thus,  5  is  a  factor  of  15.     Why  ?     What  other  factor 
has  15  ?     If  a  number  has  any  factors,  what  is  the  least 
number  of  factors  it  may  have  ?     Which  terms  in  division 
are  factors  ?     They  are  factors  of  what  ?     Which  terms  in 
multiplication    are    factors  ?     They  are    factors   of    what  ? 
When  one  factor  of  a  number  is  known,  how  can  the  other 
factor  be  found  ? 

88.  A  number  that  has  no  factors  but  itself  and  one  is  a 
Prime  Number.     Thus,  1,  3,  5,  7,  11,  13,  17,  and  19  are  prime 
numbers. 

89.  A  number  that  has  other  factors  than  itself  and  1  is 
a  Composite  Number.      Thus,  4,  9,  12,  and  21  are  composite 
numbers. 

90.  A  factor  that  is  a  prime  number  is  a  Prime  Factor. 

Thus,  2,  3,  and  5  are  prime  factors  of  30. 

91.  A  number  that  has  two  for  a  factor  is  an  Even  Num- 
ber.    Name  all  the  even  numbers  from  2  to  30. 

130 


FACTORING  131 

92.    A  number  of  which  2  is  not  a  factor  is  an  Odd  Number. 
Name  all  the  odd  numbers  from  1  to  29. 

93. 


Rule  for  finding  whether  a  Number  is  Prime  or  not 

1.  Divide  the  given  number  by  2. 

2.  If  2  gives  a/ remainder,  divide  by  3. 

3.  Continue  this  process,  using  each  prime  number 
in  order  as  a  divisor,  until  an  exact  divisor  is  found,  or 
until  the  divisor  exceeds  the  quotient.     If  no  exact  divisor 
is  found  until  the  divisor  used  exceeds  the  quotient,  the 
number  is  prime.     Otherwise  it  is  composite. 


94.    Find  whether  these  numbers  are  prime  or  composite: 

1.  143         5.    211         9.    121       13.    231        17.    437 

2.  123        6.    221      10.      97       14.    161        is.    401 

3.  324         7.    119       11.    213       15.      87        19.    593 

4.  163        8.    208      12.    215       16.      78        20.    395 

95.    Finding  the  factors  of  numbers  is  called  Factoring. 

NOTE.  —  Since  1  is  a  factor  of  every  number,  it  is  not  generally  men- 
tioned among  the  factors  of  a  number. 

1.    Find  the  prime  factors  of  1320. 
2  1320 


660 


330  By  what  kind  of  numbers  must  we  divide  ? 


lei  Why? 

55  Which  divisors  do  we  use  first  ? 

"~~jj  What  beside  the  divisors  is  a  prime  factor  ? 

2,  2,  2,  3,  5,  11.  Ans. 


132  PRIMARY  ARITHMETIC 

96. 


Rule  for  finding  the  Prime  Factors  of  a  Number 

1.  Divide  the  given  number  by  its  smallest  prime 
factor.       Divide  the   quotient  by  the  same  factor,  if 
possible,  and  repeat  the  process  as  many  times  as  that 
divisor  can  be  used. 

2.  Divide  the  last  quotient  obtained   by  the  next 
larger  prime   factor,   and   repeat  if   possible,   as  with 
the  first  prime  factor. 

3.  Continue  in  this  way  until  the  quotient  is  a  prime 
number.     All  the  divisors  and  the  last  quotient  are  the 
prime  factors  required. 


97.    Find  the  prime  factors  of  : 


l.   30 

5.  110 

9.  189 

13.   414 

2.  120 

6.  105 

10.  665 

14.  3381 

3.  42 

7.  462 

11.  429 

15.   667 

4.   66 

8.  45 

12.  425 

CANCELLATION 

98.   1.    Divide  210  by  30. 

210,  Dividend      ^    ~      ,. 

~j^-. =  7,  Quotient. 

30,  Divisor 

o-i  A      9      i  A-  f  What  is  done  to  the  dividend? 

~—^  =  -^  =  7,  Quotient.    J  To  the  divisor  ? 

[  How  does  it  affect  the  quotient  ? 

(  What  is  done  to  the  dividend? 
105°  **  -  ~    =  7,  Quotient.    J  To  the  divisor? 

[  How  does  it  affect  the  quotient  ? 

^  T  What  is  done  to  the  dividend? 

2pL2  =1        =7,  Quotient.   J  To  the  divisor  ? 

[  How  does  it  affect  the  quotient  ? 


FACTORING  133 

Dividing  both  dividend  and  divisor  by  the  same  number  affects  the 
quotient  how  ? 

210      2x3x5x7     £  x  3  x  ^  x  7 

•80s     2x3x5  ?x3x?     =  7'  Q"°tlent 

This  example  might  be  expressed  thus  : 

7 
W 

w 

%    =  7,  Quotient. 


99.    Taking  out  the  same  factor  from  both  dividend  and 
divisor  is  Cancellation. 

100.    Find    the    answers    to   the    following   questions   by 
means  of  cancellation  : 

1.  Divide  36  x  27  x  49  x  38  x  50  by  70  x  18  x  15. 

2.  (28  x  38  x  48)  -=-  (14  x  19  x  24  x  2  x  2)  =  ? 

3.  (26  x  5  x  54)  -  (13  x  5  x  6)  =  ? 

4.  What   is   the  quotient  of    36  x  48  x  16   divided   by 
27x24x8? 

5.  Divide  5  x  45  x  7  x  20  by  49  x  5  x  4  x  9. 

6.  Divide  5  x  51  x  7  x  9  x  4  by  17  x  20  x  12  x  7  x  2. 

7.  Divide  25  x  2  x  72  x  14  by  6  x  9  x  120. 

8.  How  many  bushels  of  potatoes  at  50  cents  a  bushel 
must  be  given  in  exchange  for  15  pounds  of  tea  at  40  cents 
a  pound  ? 

9.  If  60  yards  of  cloth  cost  $120,  how  many  yards  can 
be  bought  for  1  40? 

10.    15  oranges  cost  45  cents      How  much  will  7  oranges 
cost? 


134  PRIMARY   ARITHMETIC 

11.  A  dairyman  sells  100  quarts  of  milk  daily  at  5  cents 
a  quart.     How  many  bushels  of  corn  at  45  cents  a  bushel  can 
he  buy  with  10  days'  milk  receipts  ? 

12.  A  farmer  sold  a  grocer  45  bushels  of  apples  at  50  cents 
a  bushel,  taking  his  pay  in  flour  at  90  cents  a  sack.     How 
many  sacks  did  he  receive  ? 

GREATEST  COMMON  DIVISOR 

101.  A   number   that   will    exactly  divide    two    or   more 
numbers  is  a  Common  Divisor  of  those  numbers.     It  is  also 
a  Common  Factor.     Thus,  2  is  a  common  divisor  of  6  and  4 ; 
5  cents  is  a  common  divisor  of  10  cents,  25  cents,  and  15 
cents. 

102.  The  largest  number  that  will  exactly  divide  two  or 
more  numbers  is  the  Greatest  Common  Divisor  of  those  num- 
bers.    It  is  also  the  Greatest  Common  Factor.     Thus,  6  is 
the  greatest  common  divisor  of  12,  18,  and  24 ;    15  is  the 
greatest  common  divisor  of  45  and  60. 

103.  Numbers  that  have  no  common  factor  are  Prime   to 
Each  Other.     Thus,  22  and  35  are  prime  to  each  other. 

104.  Find  the  greatest  common  divisor  of  24,  36,  and  72. 

Name  the  common  factors  of 
24,  36,  and  72.     Since  2,  2,  and 

79      A      a      9      *      Q       3    are    all    the    common    factors 

of  24,  36,  and  72,  what  will 
you  do  with  2,  2,  and  3  to  find  the  greatest  common  factor  ? 
2x2x3  =  what  ?  What  is  the  greatest  common  factor  ? 
For  convenience,  we  may  find  the  common  factors  thus : 


GREATEST   COMMON   DIVISOR  135 

24,  36,  72 


3 


12,  18,  36 


6,     9,  18 


2,     3,     6 
2x2x3  =  12,  greatest  common  divisor.     Ans. 

105.    From  this  example  we  may  make  the  following 


Rule  for  finding  the  Greatest  Common  Divisor 

1.  Write  the  given  numbers  in  a  horizontal  line. 

2.  Divide  them  by  all  their  common  factors  in  suc- 
cession, beginning  with  the  smallest. 

3.  Multiply  the  common  factors  together. 


106.  Find  the  greatest  common  divisor : 

1.  84,  132  e.   40,  60,  80  11.  45,  60,  90 

2.  63,  42  7.    64,  144,  560  12.  36,  72,  81 

3.  90,  105  a    36,  48,  24  13.  44,  121,  132 

4.  112,  168  9.   40,  56,  72  14.  63,  126,  189 

5.  132,  156  10.    18,  54,  32  is.  36,  81,  135 

LEAST   COMMON   MULTIPLE 

107.  A  number  that  exactly  contains  another  number  is  a 
Multiple  of  that  number.     Thus,  30  is  a  multiple  of  10. 

108.  A  number  that  exactly  contains  two  or  more  numbers 
is  a  Common  Multiple  of  those  numbers.     Thus,  60  is  a  com- 
mon multiple  of  15,  6,  and  10. 

109.  The    smallest    number    that    exactly    contains    two 
or  more  numbers  is  the  Least  Common   Multiple  of  those 
numbers.     Thus,   30  is  the  least  common  multiple   of  15, 
6,  and  10. 


Q  ^  Q  ~  ^  we  f°un(i  ?     A  number  to  con- 

=  £ 


136  PRIMARY   ARITHMETIC 

1.    Find  the  least  common  multiple  of  60,  90,  50,  and  150. 
fin  —  9      9      3  r  What  kind  of  factors  have 

\  Q  ^  Q  ~  ^ 

X  o  X  o  X  O  .          ->_ 

__   9  55 

—  9  3  ^      ^     f  actors  ?     To  contain  90  ?     To 

contain  50  ?     To  contain  150  ? 

To  contain  60,  90,  50,  and  150,  a  number  must  contain 
how  many  factor  2's  ?  How  many  factor  3's  ?  How  many 
factor  5's  ?  What  other  factors  ?  What  is  the  smallest 
number  that  contains  2x2x3x3x5x5?  What,  then, 
is  the  least  common  multiple  of  90,  60,  50,  and  150  ? 

The  necessary  factors  may  be  conveniently  found  thus  : 


2 
3 
5 
5 

90 

50 

60 

150 

45 

25 

30 

75 

15 

25 

10 

25 

3 

5 

2 

5 

31        21 

2x3x5x5x3x2  =  900,  least  common  multiple.     Ans. 

110.    From  this  example  we  may  make  the  following 


Rule  for  finding  the  Least  Common  Multiple 

1.  Write  the  given  numbers  in  a  horizontal  line. 

2.  Divide  them  by  any  prime  number  that  will  divide 
two  or  more  of  them.      It  is  best  to  begin  with  the 
smallest. 

3.  If  any  number  will  not  exactly  contain  the  divisor, 
bring  that  number  down  into  the  line  with  the  quotients. 

4.  Continue  this  process  until  the  quotients  obtained 
are  prime  to  each  other. 

5.  Multiply  together  all  the  divisors  and  the  last  line 
of  quotients. 


INDICATED   OPERATIONS  137 

111.  Find  the  least  common  multiple  : 

1.  18,  27,  30  5.  36,  40,  48  9.  24,  42,  54,  360 

2.  9,  12,  18  6.  18,  24,  36  10.  25,  20,  35,  40 

3.  16,  48,  60  v.  15,  30,  21,  28  11.  14,  21,  35,  45 

4.  21,  27,  36  a  15,  60,  140,  210  12.  24,  48,  96,  192 

INDICATED   OPERATIONS 

112.  The  Parenthesis  ()  indicates  that  all  the  numbers 
included  therein  are  to  be  subjected  to  the  same  operation. 

Thus,  (17  —  6)  x  2  indicates  that  the  difference  between  6 
and  17  is  to  be  multiplied  by  2.  17  -  6  =  11.  11  x  2  =  22. 
Without  the  parenthesis,  this  would-be  17  —  6  x  2,  and  indi- 
cates that  2  x  6  is  to  be  taken  from  17.  17  —  11  =  6. 

(4  +  8)  -T-  4  indicates  that  the  sum  of  8  and  4  is  to  be 
divided  by  4.  The  result  is  3.  If  the  parenthesis  is  omitted, 
we  have  4  +  8-5-4,  which  indicates  that  8  -T-  4,  or  2,  is  to  be 
added  to  4.  4  +  4  =  8. 

[(6  +  5)  x  4  +  6]  -T-  10  indicates  that  6  +  5  is  to  be  multi- 
plied by  4,  6  added  to  the  product,  and  the  sum  divided  by  10. 
6  +  5  =  11.  11  x  4  =  44.  44  +  6  =  50.  50  -  10  =  5. 

113.  Brackets  [  ]  and  the  Vinculum  "       "  have  the  same 
uses  as  the  parenthesis. 

[3  +  4]  x  3,  3  +  4x3,  mean  the  same  as  (3  +  4)  x  3. 

When  the  parenthesis  or  vinculum  is  included  within  the 
brackets,  the  operations  indicated  within  the  parenthesis  or 
under  the  vinculum  should  be  performed  first. 

114.  When  the  parenthesis,  vinculum,  or  brackets  are  not 
used,  or  after  they  have  been  removed,  operations  indicated 
by  x  or  -i-  must  be  performed  first,  then  the  operations  indi- 
cated by  +  and  - .     Thus,  12-5-4x2  +  36  --4-2x4  =  ? 

SOLUTION.  —  12-4x2  =  6.  36  -  4  =  9.  2x4  =  8.  The  statement 
now  reads,  6  +  9—8.  The  result  is  7, 


138  PRIMARY    ARITHMETIC 

115. 

1.  4  +  3x2  =  ?  4.    4  x  (3  +  2)  =  ? 

2.  (4  +  3)  x  2  =  ?  5.    8  +  4  -r-  2  =  ? 

3.  4x3  +  2  =  ?  6.    (8  +  4)-2  =  ? 

Find  the  value  of  : 

7.  15  +  3x6  +  10-5. 

a  (6  +  4)  x  (3  +  2)  -  (8  x  5). 

9.  18-3  +  2  +  8x2  +  14-6. 

10.  2  +  12  -5-4  -(10  +  16-5-4)  -5-7. 

11.  11  +  4  -3  +  6x4. 

12.  3  +  4  x  6-*-  (15  -18-*-  3). 

13.  164  +  16-250-10  +  16x3. 

14.  17  +3x4x6  +  3-5-3  +  3. 

is.  [39  +  8  -*-  2  +  7]  x  6. 

16.  [6  +  15  x  3  -  6  +  16  -*-  8  +  4]  -  3  +  5. 


17.    7  +  8      10-2.  18. 


19. 


4 

20.  Indicate  the  addition  of  36,  15,  16,  38. 

21.  Indicate  in  two  ways  the  division  of  16  by  4.       Of 

5  +  17  divided  by  11. 

Indicate  the  operations  of  the  following  problems  : 

22.  A  lady  found  3  roses  on  one  bush,  5  on  another,  and 
7  on  another.     How  many  roses  did  she  find  ? 

23.  James  found  2  eggs  in  a  hen's  nest,  5  in  another,  and 

6  in  another.     How  many  eggs  did  he  find  in  all  ? 


INDICATED   OPERATIONS  139 

24.  A  man  spent  $10.16  on  Monday  and  $4.40  on  Tues- 
day.     How  much  more  did  he  spend  on  Monday  than  on 
Tuesday  ? 

25.  A  boy  had  36  marbles.     He  lost  6  one  day  and  11  the 
next.     How  many  had  he  left  ? 

36  -(6  +  11)  =  ? 

26.  If  you  have  60  cents  and  spend  18  cents  for  ribbon 
and  12  cents  for  thread,  how  much  have  you  left  ? 

27.  James  had  18  marbles  and  found  5  more.     He  after- 
ward lost  8  marbles.     How  many  were  left  ? 

28.  A  boy  deposited  $1  in  the  savings  bank  on  the  1st  of 
the  month,  75^  on  the  10th,  and  $2.50  on  the  25th.     On 
the  30th  he  drew  out  $2.75.     How  much  was  left  in  the 
bank? 

29.  John  had  $5.18  in  the  bank.     He  drew  out  $1.50  on 
Monday  and  $.75  on  Tuesday.     How  much  had  he  left? 

30.  4  increased  by  the  product  of  3  and  2. 

31.  The  sum  of  4  and  3,  multiplied  by  2. 

32.  The  product  of  4  and  3,  increased  by  2. 

33.  4  multiplied  by  the  sum  of  3  and  2. 

34.  84  less  the  product  of  5  and  6. 

35.  The  difference  between  72  and  42,  multiplied  by  4. 

36.  144  subtracted  from  the  product  of  18  and  18. 

37.  6  multiplied  by  the  difference  between  11  and  6. 

38.  Henry  has  58  ^,  and  John  63  ^.     Charles  has  4  times 
as  much  as  both.     How  much  has  Charles  ? 

39.  Lucy  and   Mary  went  shopping.     Lucy  bought  lace 
for  55^,  and  Mary  5  yards  of  ribbon  at  15^  a  yard.     What 
was  the  amount  of  both  purchases  ? 


FRACTIONS 


_Ji | ^_ 


H * , M , M. 


116.  Draw  a  line.     Divide  it  into  2  equal  parts.     What  is 
one  of  these  parts  ?     How  many  halves  in  the  line  ? 

Draw  another  line.  Divide  it  into  3 'equal  parts.  What 
is  one  part  ?  How  many  thirds  in  the  line  ? 

Draw  another  line.  Divide  it  into  4  equal  parts.  What 
is  one  part  ?  How  many  fourths  in  the  line  ? 

Draw  another  line.  Divide  it  into  5  equal  parts.  One 
of  these  parts  is  what  ?  Two  of  them  are  what  ?  Three  of 
them  ?  Four  of  them  ?  All  of  them  ? 

Which  is  larger,  |  or  \  ?  \  or  \  ? 

117.  Make  a  square.     Draw  a  line  through  the  middle  of 
it  from  corner  to  corner.     Into  how  many  parts  have  you 
divided  the  square  ?     What  is  one  part  ? 

Connect  the  other  corners  by  a  line.  Into  how  many 
parts  is  the  square  now  divided  ?  What  is  one  of  the  parts 
called  ?  What  are  two  of  them  called  ?  Three  of  them  ? 

140 


FRACTIONS 


141 


118.  Which  piece  of  this  pie  would  you  rather  have,  |,  |, 
1,  or  |  ?  Why  ? 

One  piece  of  the  last  pie  is  what  part  of  it  ?  two  pieces  ? 
8  pieces  ?  5  pieces  ? 


Write  the  number  that 
represents  1  part  of  this 
pear.  Two  parts.  Write 
the  number  that  repre- 
sents the  whole  pear. 


How  many  small  squares  are  there 
in  the  large  square  ?  One  of  the  small 
squares  is  what  part  of  the  large  square  ? 
What  part  of  the  large  square  is  yellow  ? 
White  ?  Yellow  and  white  ?  How  many 
ninths  of  the  large  square  are  red  ?  What 
part  of  the  large  square  is  blue  ? 


142 


PRIMARY   ARITHMETIC 


How  many  oblongs  are  here  ? 

How  many  circles  ? 

One  oblong  is  what  part  of  all  the  oblongs. 

What  part  of  all  the  circles  are  in  one  oblong  ? 

^  of  all  the  circles  are  how  many  circles?  ^  of 
8  =  ?  |  =  ?  8  H-  4  =  ? 

What  part  of  all  the  circles  are  red  ?  White  ? 
Yellow  ?  Green  ?  Red  and  white  ? 

•J  of  all  the  circles  are  how  many  circles  ?  J- 
=  how  many  ?  |  =  how  many  ? 

119.  A  Fraction  is  one  or  more  of  the  equal 
parts  of  any  thing.     Thus,  ^  of  an  inch  ;  -f^- ;    * . 

120.  A  fraction  is  also  an  expression  of  divi- 
sion.    Thus,   -|  means  1-5-4,   or  1   whole  thing 


divided  into  4  equal  parts. 
24  divided  into  3  equal  parts. 


•  means  24  -^-  3,  or 


121.  The  number  below  the  line  in  a  fraction 
is  the  Denominator.  v    It  tells  the  number  of  parts 
into  which  the  whole  is  divided.     Thus,  9  is  the 
denominator  of  ^. 

122.  The  number  above  the  line  in  a  fraction 
is  the  Numerator.     It  tells  the  number  of  parts 
used.     Thus,  3  is  the  numerator  of  f  . 


123.  The  numerator  and  denominator  are  the  Terms  of  a 
Fraction.     What  are  the  terms  of  J  ?  of  f  ?  of  |  ?  of  f  f  ? 

124.  The  quotient  of  the  numerator  divided  by  the  de- 
nominator is  the  Value  of  the  Fraction.     What  is  the  value 
off?  off?  of  J^-?  of  -%5-?  off? 


REDUCTION   OF   FRACTIONS 
125.    Read  the  following  fractions  : 

2.  |  6.     f  10.     T\  14. 

3.  f  7.     1  11.     £  15. 

4.  I  8.     |  12.     2*0  16' 


143 


126.    Write  in  figures  : 

17.  Four-fifths. 

18.  Seven-ninths. 

19.  Five-eighths. 

20.  Six-tenths. 

21.  Four-elevenths. 

22.  Six-thirteenths. 

23.  Four  twenty-firsts. 

24.  Sixteen  twenty-seconds. 

25.  Fifteen  twenty-fifths. 

26.  Sixteen  forty-fourths. 


27.  Eight  thirty-thirds. 

28.  Six  fifty-fourths. 

29.  Seventeen  sixty-ninths. 

30.  Seven  ninety-eighths. 

31.  Twenty-four  eightieths. 

32.  Seven  fiftieths. 

33.  Sixty-five  seventieths. 

34.  10  one-hundred-fifths. 

35.  12  two-hundred-eighths. 


REDUCTION   OF  FRACTIONS 
Reduction  of  Fractions  to  Lowest  Terms 

127.  Reduction  is  changing  the  form  of  numbers  without 
changing  their  value.     Thus,  f  =  1 ;   10  cents  =  1  dime. 

128.  Fractions  are  in  their  Lowest  Terms  when  the  numer- 
ator and  denominator  have  no  common  divisor.     Thus,  |  is 
in  its  lowest  terms.     -     is  not  in  its  lowest  terms. 


144 


PRIMARY   ARITHMETIC 
FIRST    ILLUSTRATION 


How  many  squares  are  there  in  the  oblong  ? 

One  square  is  what  part  of  the  oblong  ? 

How  many  squares  are  red  ? 

How  many  ninths  are  red  ? 

How  many  colors  are  there  in  the  oblong  ? 

Into  how  many  parts  do  the  colors  divide  the  oblong? 
How  do  these  parts  compare  ?  One  of  these  parts  is  what 
fraction  of  the  oblong  ?  What  fraction  of  the  oblong  is  red  ? 
How  many  ninths  are  red  ?  How  does  |  compare  with  J  ? 
Write  |  =  ^. 

What  could  you  do  to  3  to  get  1  ? 

What  could  'you  do  to  9  to  get  3  ? 

What  would  you  do  to  |  to  get  ^  ? 

Dividing  both  terms  of  a  fraction'  by  the  same  number 
affects  the  value  of  the  fraction  how  ? 

The  terms  of  ^  have  what  common  divisor  ?  Then  ^  has 
been  reduced  to  what?  (See  definition,  Art.  128.) 

SECOND    ILLUSTRATION 

Into  how  many  equal  parts  is  this  circle 
divided  by  the  black  lines  ?     What  is  one 
of  the  8  equal  parts  called  ?     What  part 
of  the  circle  is  green  ?     How  many  eighths 
are  in  the*  green  half  ?      -|  of  the  circle 
compares  how  with  J  ?     What  must  you 
do  with  4  and  8  in  the  fraction  |-  to  make 
it  ^  ?     The  terms  of  J  have  what  common  divisor  ? 
Then  -|  has  been  reduced  to  what  ? 


REDUCTION  OF  FRACTIONS 


145 


129.  Show  by  these  cir- 
cles that  |  =  f  That  £  =  f. 


ThatT<V=f. 


How  are  these  fractions 
reduced  to  lowest  terms? 

130. 


Rule  for  Reduction  of  Fractions  to  Lowest  Terms 

Divide  both  numerator  and  denominator  by  common 
divisors  until  they  become  prime  to  each  other. 


The  numerator  of  a  fraction  is  which  term  of  division  ? 
The  denominator  ?  The  value  of  the  fraction  ? 

Dividing  both  dividend  and  divisor  by  the  same  number  af- 
fects the  quotient  how  ?*  (See  Cancellation,  article  No.  103.) 

Dividing  both  numerator  and  denominator  of  a  fraction  by 
the  same  number  affects  the  value  of  the  fraction  how  ? 

Change  the  following  to  their  lowest  terms  : 


131.  Mental. 

1-  I  *•    I 

2-  I          5-  H 

3.     If  6.     If 

132.  Written. 

1-    tl  *•    tt 


7-    I* 

8.  ff 

9.  || 


10. 
11. 


13. 


•     li 


2- 

3- 


6. 


7. 
8. 
9. 


_72 
12  S 


12. 


146  PRIMARY   ARITHMETIC 


""    m  21.    T¥&  25. 

18      TVs  22.     $fa  26.     Kf 

19'     A\  23.     |fl  27.     fOf 

«•     Hi  20.     &$  24.     ^  28.     1|| 

29.  Express  in  lowest  terms  230  -T-  345. 

30.  Express  in  lowest  terms  98  divided  by  392. 

31.  Express  in  lowest  terms  437  -s-  2485. 

32.  Express  in  lowest  terms  the  quotient  of  288  divided 
by  504. 

33.  What  are  the  lowest  terms  of  iff  ? 

Reduction  of  Integers  and  Mixed  Numbers  to  Fractions 

133.  A  number  that  is  composed  of  whole  units  only  is  an 
Integer.     Thus,  5,  4,  1,  13,  and  2000  are  integers. 

134.  A  number  that  is  composed  of  an  integer  and  a  frac- 
tion is  a  Mixed  Number.     Thus  8|,  *  9T^,  and  3|  are  mixed 
numbers. 


How  many  fourths  in  1  circle  ?  In  2  circles  ?  In  3  circles  ? 
In  4  circles  ?  How  do  you  find  it  ? 

How  many  fourths  in  4|  circles  ?  In  2|-  circles  ?  In  3| 
circles  ?  How  do  you  find  it  ? 

How  many  eighths  in  1  circle  ?  In  3  circles  ?  In  2  circles  ? 
In  4|  circles  ?  In  2|  circles  ?  How  do  you  find  it  ? 

How  do  you  reduce  an  integer  or  a  mixed  number  to  a 
fraction  ? 


REDUCTION   OF   FRACTIONS  147 

135. 

Rule  for  Reduction  of  Integers  and  Mixed  Numbers 
to  Fractions 

1.  Multiply  the  integer  by  the  denominator  of  the 
required  fraction. 

2.  Add  to  the  product  the  numerator  of  the  given 
fraction,  if  there  is  one. 

3.  Use  this  result  as  the  numerator  of  the  required 
fraction. 

4.  For  a  denominator,  take  the  denominator  of  the 
given  fraction  or  fraction  required. 

Reduce  the  following  to  fractions : 
136.    Mental. 


1. 

H 

5. 

H 

9. 

Q  4 

&W 

13. 

89 

2. 

41 

6. 

2f 

10. 

49 

14. 

7T\ 

3. 

3f 

7. 

*t 

11. 

5! 

15. 

8T^ 

4. 

&i 

8. 

2| 

12. 

6f 

16. 

•i 

137. 

Written. 

17. 

251 

24. 

37T% 

31. 

270|| 

38. 

491^ 

18. 

9T\ 

25. 

49175 

32. 

1912 

39. 

355T 

19. 

17i 

26. 

253T 

33. 

29T4i 

40. 

191^ 

20. 

25f 

27. 

59& 

34. 

149f 

41. 

203T% 

21. 

15A 

28. 

67T56 

35. 

128| 

42. 

98H 

22. 

23A 

29. 

S9fi 

36. 

137^ 

43. 

87i| 

23. 

40* 

30. 

131^ 

37. 

238H 

44. 

138^ 

148  PRIMARY   ARITHMETIC 

'  Reduction  of  Fractions  to  Integers  or  Mixed  Numbers 

138.  A  fraction  whose  numerator  is  smaller  than  its  de- 
nominator is  a  Proper  Fraction.     Thus,  |,  f ,  and  £-§•  are  proper 
fractions. 

139.  A  fraction  whose  numerator  equals  or  exceeds  its 
denominator  is  an  Improper  Fraction.     Thus,  f,  -^-,  ^-,  and 
-^L  are  improper  fractions. 

140.  A  boy  has  two  half  dollars.     That  is  the  same  as 
how  many  whole  dollars  ?     Six  half  dollars  equal  how  many 
whole  dollars  ?     How  do  you  find  it  ? 

Eleven  half  dollars  make  how  many  dollars  and  how  many 
halves  over?  How  do  you  find  it  ?  Write  it. 

How  many  quarters  make  a  dollar  ? 

How  many  dollars  would  8  quarters  make  ?     40  quarters  ? 

Fifteen  quarters  make  how  many  dollars  and  how  many 
quarters  over  ?  Write  it.  How  do  you  find  it  ? 

|  =  how  many  whole  ones  ?  |-  ?  -^-  ?  |-  ? 

.|  =  how  many  wholes  ?  ^  ?  -^  ?   i^l  ? 

A  fraction  is  an  expression  of  what  operation  ? 

How  do  you  find  the  value  of  a  fraction  ? 


Rule  for  Reduction  of  a  Fraction  to  an  Integer  or  a 

Mixed  Number 
Divide  the  numerator  by  the  denominator. 


141.    Mental.     Find  the  values  of  : 

1.  |          5.    Jjp-           9.    If-        13.    If-  17.  21JL          21.    f| 

2.  f          6.    I           10.    -^         14.    f^  18.  {J             22.    f| 

3.  f          7.    Jj/L         11.    -*/        15.    -V-  19.  ff             23.    ff 

4.  8.         -         12.    -.        16.    IA  20.  24. 


REDUCTION   OF   FRACTIONS  149 

142.    Written.     Reduce  to  whole  or  mixed  numbers: 

1.     JL  3.     ^2  5.     -Mf  7.     JLBL  9. 

4-  6-      -      8- 


11.     -V_3-  14.     £4£8.  17.     W  20. 

1  o  o  »  'to 


12. 

13.  L  16.     2  19.  2-  22. 


To  Least  Common  Denominator 

143.  Fractions   whose    denominators    are    alike    have    a 
Common  Denominator.     Thus,  ^,  |~|,  and  ||-  have  a  common 
denominator. 

144.  Fractions  having  the  smallest  possible  common  de- 
nominator   are  said   to  have  their  Least  Common  Denomi- 
nator.    Thus,  2^,  ^,  ^,  and  |^  have  their  least  common 
denominator. 

145.  Multiplying  both  dividend  and  divisor  by  the  same 
number  affects  the  quotient  how  ?     Multiplying  both  terms 
of  a  fraction  by  the  same  number  affects  the  value  of  the 
fraction  how  ? 

1.  Reduce  J,  |,  |,  and  |  to  fractions  whose  denominator 
is  120. 

|  =  y6^.  What  must  you  do  with  the  denominator  2 
to  make  it  120  ?  If  you  multiply  2  by  60,  what  must  you 
do  with  the  numerator  so  that  the  value  of  the  fraction  may 
not  be  changed  ? 

J  =  -j^j-.  By  what  must  you  multiply  the  terms  of  f  to 
reduce  it  to  120ths  ?  How  do  you  find  that  number  to  be 
40? 


150  PRIMARY   ARITHMETIC 

I  =  i%V  -^y  what  must  you  multiply  the  terms  of  |  to 
make  it  -££$  ?  How  do  you  find  that  number  to  be  30  ? 

|  =  y4^.  By  what  must  you  multiply  the  terms  of  f  to 
make  it  T4^-  ?  How  do  you  find*that  number  to  be  24  ? 

Since  the  common  denominator  must  be  divided  by  the 
denominators  of  all  the  given  fractions,  it  must  be  what  of 
their  denominators  ? 

Then  the  least  common  denominator  must  be  what  of  the 
given  denominators  ? 

These  questions  suggest  the  following 


Rule  for  Reduction  of  Fractions  to  their  Least  Common 
Denominator 

1.  Find  the  least  common  multiple  of  the  denomi- 
nators of  the  given  fractions.     This  is  the  least  common 
denominator. 

2.  Divide  the  least  common  denominator  by  the  de- 
nominator of  the  first  of  the  given  fractions.     Multiply 
its  numerator  by  the  quotient  obtained.     The  product 
is  the  required  numerator. 

3.  Proceed  in  the  same  way  with  each  of  the  given 
fractions. 


THE    RULE    ILLUSTRATED 

35  2 

2.    Reduce   -    -  and  -t'-  to  their   least   common   denomi- 

4    o  o 

nators. 


4 

6 

3 

=  12, 

least  common 

denominator. 

2 

3 

3 

X 

2 

xl 

xl 

ADDITION   OF   FRACTIONS 


151 


How  many  12ths  in 
How  many  12ths  in 


4x3 


How  many  12ths  in 
How  many  12ths  in 


(12-6  = 

/5x2  _  10. 
~~         * 


How  many  12ths  in  £?     (12  —  3  =  4.^ 
How  many  12ths  in  |  ?     (f-£j  =  -f-% •) 


Change  the  following  to  fractions  having  a  least  common 
denominator : 


146. 

Mental. 

1.    |, 

f 

4-     f  ,  TV  2^ 

7. 

1'  i  iV 

2.    |, 

f 

5.     1,  1,  T^ 

8. 

i.  I'  f 

3.    J, 

$ 

e.  J,  f  ,  Jy 

9. 

5'   6^  i- 

147. 

Written. 

1.   J, 

3     5 
5'   6 

5.    1    |,  f  ,  T^ 

9. 

f>  1'   9'  10 

2.    f, 

1'    9 

6.    I,  |,  f  ,  | 

10. 

f  '  A'  1'  1 

3.    f, 

T90>  J 

7-    9,f,TVf 

11. 

f  i  fr  A 

4.    $, 

I'   2 

8-     J,f  fA 

12. 

f  f  i  tf 

152  PRIMARY    ARITHMETIC 


ADDITION   OF   FRACTIONS 

148.  A  proper  fraction  is  in  its  simplest  form  when  it  is 
in  its  lowest  terms. 

An  improper  fraction  is  in  its  simplest  form  when  it  is 
reduced  to  an  integer  or  a  mixed  number. 

1*.  ,  Add  £  and  A.    £  +  £  _  «±«  _  £  _  £.     An,. 

,,,362        ,1 

2.  Add  -,  -,   -,  and  -. 

|  +  |  +  2  +  l  =  8±«±l±l  =  ^  =  8.     Ans. 

23  5 

3.  Add    -,    -,  and  —  . 

o     4  lo 


•7 


2,3,5      32  ,  36  ,  15     32  +  36  4-  15     83 

3  +  4  +  l6  =  r8  +  48  +  r8  =  -  ~48  -  =48 


328 


X3xl  x4  =  48 

Why  do  we  reduce  these  fractions  to  their  least  common 
denominator  ? 

150.    The  above  examples  illustrate  the  following 


Rule  for  Addition  of  Fractions 

1.  Reduce  the  fractions  to  their  least  common  de- 
nominator. 

2.  Add  the  new  numerators,  and  write  the  sum  over 
the  least  common  denominator. 

3.  Reduce  the  result  to  its  simplest  form. 


ADDITION   OF   FRACTIONS  153 


151.    Addition  of  Mixed  Numbers. 

l.    Add  3f,  5i  and 


152. 


=  =          =          .      Ans. 


Rule  for  Addition  of  Mixed  Numbers 

1.  Add  the  integers  and  fractions  separately. 

2.  Unite  the  sum  of  the  integers  and  the  sum  of  the 
fractions. 

3.  Reduce  the  result  to  its  simplest  form. 


153.  Mental.     Add  the  following: 

1-  i,   *             5.     1,   1              9.     f,   £,   3  13.     11,    21,    1 

2.  |,    1.             6.     f,    1             10.     1,    1,    11  14.     3J,    If,    5 

3.  f,  I          7.    l,  i          11.    21,  41,  1  15.    f,  31   4 
4-     |,   §            8-    i,    J            12.     l,    1,   £  16.     2|,  3|,  21 

17.  A  man  paid  $f  for  a  book,  f  |  for  an  inkstand,  and 
$  \  for  writing  paper.     How  much  did  he  spend  ? 

18.  Mary  has  $|;  her  mother  gave  her  $3£.     How  much 
has  she  ? 

154.  Written.     Addition : 

1.    f,  Jj,   |                    7.     |,  ft,  &,  1  13.     1,   2f,   |,   6 

2-  \,   A,   A                     8.     |,  |,  ^j,  ^  14.     f,    |,    2|,    ^ 

3-  f,    i    ^                    9-     i,    f,    |,    J  15.     4|,   f,   |,    /T 
*•     f'    f,    I                    10.     f,    i    6,    |  16.     f,    J,   T^,   4 
5.     £,    1,   |                  11.     |,   A     ^,   |  17.     6|,    8|,    f,    I 
6-     i    ^    L   T36            12-     f,    A,    |,   i  18-     3,    f,    },   | 


154  PRIMARY   ARITHMETIC 

19.    f,  4,  f,  1|       21.    6§,  8J,  5|,  7f    23.    j,  f,  f,  |, 

20-    I'  I  iV  T85     22-    9i>  5f'  9'  H       2*-    5},  7|,  91,  45 

25.  14f,  9|,  10J,  12if 

26.  A  man  travels  25|  miles  on   Monday,  37^  miles  on 
Tuesday,  on  Wednesday  as  many  miles  as  on  Monday  and 
Tuesday.     How  many  miles  does  he  travel  in  three  days  ?* 

27.  A  farmer  has  27^  bushels  of  potatoes  in  one  bin,  133$ 
bushels  in  another,  47T5^  bushels  in  another.     How  many 
bushels  has  he? 

28.  Mr.  Brown  has  $13'0f-;  his  wife  $25f  more  than  he 
has ;  his  son  $78T9?,  and  his  daughter  $5|  more  than  his  son. 
How  much  have  all  ? 

29.  How  many  yards  of  cloth  will  I  have,  if  I  buy  123£ 
yards,  76|  yards,  and  58|  yards  ? 

30.  6^  yards  of  cloth  are  required  for  a  coat,  3|  yards  for 
trousers,  and  ^   yards   for   a    vest.      How  many  yards  are 
required  ? 

31.  Find  what  your  mother  spends  if  she  pays  1 8^  for 
your  coat,  $9J  for  your  dress,  §4|  for  your  hat,  f  2|  for  your 
shoes,  and  $1^  for  your  gloves. 

32.  How  much  land  in  a  farm  of  five  fields  if  the  first  con- 
tains 26i^  acres,  the  second  50|-|  acres,  the  third  41^  acres, 
the  fourth  69|  acres,  and  the  fifth  52|  acres  ? 

SUBTRACTION   OF   FRACTIONS 
155.   1.    From  f  take  ^V 

8  _  _7_  =  80  _  21  =  59 

3 [9 30  ""90      90  ""90*    An$* 

x  3  x  10  =  90 


SUBTRACTION    OF   FRACTIONS  155 

Rule  for  Subtraction  of  Fractions 

1.  Reduce  the  fractions  to  their  least  common  denomi- 
nator. 

2.  Subtract  the  numerator  of  the  subtrahend  from 
that  of  the  minuend  and  write  the  result  over  the  least 
common  denominator. 

3.  Reduce  to  simplest  form. 


SUBTRACTION   OF  MIXED  NUMBERS 
156.   1.    From  10^  take  3||. 


6ff     Ans. 


Rule  for  Subtraction  of  Mixed  Numbers 

1.  Subtract  the  integers  and  fractions  separately.  If 
the  fraction  in  the  minuend  is  smaller  than  the  fraction 
in  the  subtrahend,  take  1  from  the  integer  of  the  minu- 
end and  add  its  value  to  the  fraction  of  the  minuend, 
before  subtracting. 


157.   Mental.  Subtraction : 

1.  f-i  5.    T\-f         9.  7-      1  13.  4      -1£ 

2.  |-i  6.     f- 1      10.  8-    f  14.  6J-4f 
4-   i-*  8-   «-i     12-  22~i!  16'  19* -9* 


158. 

Written. 

1 

• 

|- 

i 

6. 

15 

-2J 

2 

• 

H 

I 

7. 

8* 

-4i 

3 

• 

1- 

i 

8. 

10 

5 
f 

4 

• 

<j 

— 

i 

9. 

12J 

-6J 

5 

, 

3 

I 

10. 

81 

-41 

156  PRIMARY   ARITHMETIC 


11.  if-f 

12.  f-1 

13.  JL-f 

14.  11-1 

is.    if-i 

16.  Take  l  from  f  .     From  1|  take  T9T. 

17.  From  the  sum  of  |  and  -|  take  their  difference. 

18.  What  must  I  add  to  9|  to  make  20T8^  ? 

19.  The  sum  of  two  fractions  is  i|  ;  one  of  the  fractions 
is  f  .  What  is  the  other  ? 

MULTIPLICATION   OF  FRACTIONS 

159.  A  fraction  is  an  expression  of  what  operation?  The 
numerator  of  a  fraction  is  which  term  in  division?  The 
denominator  ?  The  value  of  the  fraction  ? 


Principles 

1.  Multiplying  the  dividend  multiplies  the  quotient. 
Therefore,  multiplying  the  numerator  multiplies  the 
value  of  the  fraction. 

2.  Multiplying    the    divisor    divides  the    quotient. 
Therefore,   multiplying   the    denominator   divides   the 
value  of  the  fraction. 

3.  Dividing    the    dividend    divides    the    quotient. 
Therefore,  dividing  the  numerator  divides  the  value  of 
the  fraction. 

4.  Dividing   the    divisor   multiplies    the     quotient. 
Therefore,  dividing  the  denominator  multiplies  the  value 
of  the  fraction. 


MULTIPLICATION   OF   FRACTIONS  157 

In  what  two  ways  may  the  value  of  a  fraction  be  multi- 
plied?    Divided? 

1.    Multiply  A  by  8. 
lo 


State  the  principles  applied  in  these  operations. 
160. 


Rule  for  Multiplication  of  Fractions  by  Integers 

1.  Multiply  the  numerator  of  the  fraction  by  the  in- 
teger;    or,  divide  the  denominator  of  the  fraction  by 
the  integer. 

2.  Reduce  the  result  to  its  simplest  form. 


161.    Mental.     Multiply: 

1.  I  by  2       5.  |  by  5        9.    f  by  6       13.  ^.  by  4 

2.  |  by  4       6.   f  by  7      10.    f  by  4       14.    |  by  3 

3.  |  by  3       7.   |  by  9      11.  ^  by  5       15.  ^  by  5 

4.  |  by  3       8.  I  by  2      12.    f   by  6 

16.  At  $  I  each,  what  will  8  books  cost  ? 

17.  If  a  horse  eat  |  bushel  of  oats  in  a  week,  how  much 
will  he  eat  in  4  weeks  ? 

18.  If  a  pound  of  tea  costs  $  f ,  what  will  6  pounds  cost  ? 

19.  Multiply  the  following  fractions  by  3  and  give  the 
result  in  its  simplest  form  :  f,  |,  |,  f ,  £,  f . 

Multiply  the  fractions  in  example  19  by  5  ;  by  6 ;  by  10. 


158  PRIMARY   ARITHMETIC 


162 

.  Written.    Multiply: 

1. 

if 

by 

7 

7. 

H  by 

6 

13. 

t 

* 

by 

10 

2. 

| 

by 

6 

8. 

A  by 

10 

14. 

1 

i 

by 

12 

3. 

2T 

by 

5 

9. 

M  by 

•  7 

15. 

i 

*s 

by 

11 

4. 

u 

by 

7 

10. 

11  by 

6 

16. 

\ 

by 

20 

5. 

H 

by 

9 

11. 

A  by 

15 

17. 

§ 

\ 

by 

18 

6. 

1! 

by 

8 

12. 

A  by 

25 

18. 

1 

9 

by 

26 

19.  f  of  12  ==  ? 

SOLUTION.  —  J  of  12  =  -\2-  =  3. 

}  of  12  =  3  x  3  =  9.     Ans. 

20.  |   of   7  =  ? 

SOLUTION.  —  J  of  7  =  J. 

|  of  7  =  5  times  J  =  ¥  =  4f-     ^ns- 

NOTE.  —  |  q/"  7  is  the  same  as  f  ^wes  7,  and  the  product  is  the  same 
as  7  times  f  . 

21.  f  of  5  =  ?     -^  of  4  =  ?     |  of  3  =  ?     §  of  6  =  ? 

22.  $  10  multiplied  by  |  =  ?     ^  x  10  =  ? 

23.  f  x  8  =  ?     4  x  f  =  ?     f  x  4  =  ? 

24.  Multiply  18|  by  8,  first  reducing  the  mixed  number 
to  an  improper  fraction. 

25.  Multiply  18|  by  8  without  reducing  the  mixed  number 
to  an  improper  fraction.     First  multiply  the  fraction,  then 
the  integer,  by  8,  and  add  the  products.     Thus  : 

18* 

g  SOLUTION.  — 

8  times  f  =  ^  =  6 
8  times  18  =     144 

144  150 

150 

26.  16|  multiplied  by  10.         29.    Multiply  27  jf  by  38. 

27.  126|  multiplied  by  9.         30.    Multiply  35J|  by  46. 

28.  326|  multiplied  by  5.         31.    9  times  2lf  f  =  ? 


MULTIPLICATION   OF   FRACTIONS  159 

32.  Multiply  47  by  6|,  first  reducing  the  mixed  number  to 
an  improper  fraction. 

33.  Multiply  65  by  7-|.  35.   4$  times  48  =  ? 

34.  Multiply  125  by  14|.  36.    19f  times  385  =  ? 

163.      l.    Multiply  f  by  f . 

Since  ^  means  5  divided  by  7,  then  to  multiply  f  by  f-  is 
to  multiply  it  by  5  and  divide  it  by  7.     What  is  the  easiest 

way  to  multiply  f  by  5  ?    f— £— Y     To   divide   it   by    7  ? 

2  x  5\  .  3 

See  principles,  Article  164.     Therefore 


4 

How  was  the  work  shortened  in  examples  2  and  3  ? 

164.    These  examples  illustrate  the  following 


Rule  for  Multiplication  of  a  Fraction  by  a  Fraction 

1.  Multiply  all  the  numerators  together. 

2.  Multiply  all  the  denominators  together. 

3.  Cancel  when  possible. 

4.  Write  the  first  product  over  the  second  and  reduce 
to  simplest  form. 


160  PRIMARY   ARITHMETIC 

KOTE  1.  —  Any  integer  may  be  expressed  as  a  fraction  by  writing  it 
over  the  denominator  1. 

NOTE  2.  —  The  word  of  between  fractions  means  the  same  as  the  sign 
of  multiplication. 

Fractions  joined  by  of  form  a  Compound  Fraction. 

NOTE  3.  —  Mixed  numbers  must   be  changed  to  improper  fractions 
before  multiplying  them  together. 

Oral. 

1.  How  much  is  |  of  ^  of  an  inch  ? 

2.  Illustrate  that  \  of  \  of  an  apple  is  J  of  an  apple. 

3.  Multiply  f  by  1 ;   |  by  1;   1  by  I;    J  by  f 

4.  How  much  is  \  of  f  ?     f  of  f  ?     \  of  |  ?     l  of  T\  =  ? 

5.  A  man  owned  f  of  a  farm  and  sold  |   of  his  share. 
What  part  of  the  farm  did  he  sell  ? 

6.  James  had  $  |,  and  John  \  as  much.      How  much  had 
both  ? 

7.  If  a  pound  of  tea  costs  $  |,  what  will  \  pound  cost  ? 

165.    Written.     Find  the  products : 


1. 

2. 
3. 

4. 

1  x| 

i.'kf 

T90   X  | 

i  of  A 

7. 
8. 
9. 
10. 

1 
i 

of 
of 

V  x 

T90  ^  | 
12    X   7- 

9X4 

13. 
14. 
15. 
16. 

5f 

71 

»i 

X 
X 
X 

X 

2|  x  20 
ii  x  T5i 

5. 

|-of 

ii 

11. 

9     \x    1  0    v    8 

2T      X     -J-     X       g 

17. 

A 

X 

4   x  5| 

6. 

A* 

:i9* 

12. 

1 

f  x 

34  x  f 

18. 

A 

X 

80  x  5J 

Find  the 

value  : 

19. 

!°f 

40 

22. 

1 

of 

328 

25. 

11 

of 

342 

20. 

f  of 

42 

23. 

f 

of 

721 

26. 

15 
16 

of 

800 

21. 

f  of 

16 

24. 

1 

of 

90 

27. 

A 

of 

2222 

, 


DIVISION  OF   FRACTION  161 


28.  |  of  |  of  f  of  f  of  -|  =  ?     $  of  f  of  -V-  of  T\  =  ? 

29.  ^Offfof^oflf  Of|  =  ?      f  Of  Jf  Of  |  Of  If  =  ? 

30.  Mr.   Brown  earns  $40|   a  month,  and  his  son  |   as 
much.     How  much  does  the  son  earn  ? 

31.  At  $  12|  a  ton,  how  much  will  9^  tons  of  hay  cost  ? 

32.  What  will  be  thg  cost  of  48|  yards  of  cloth  at  $  |  a 
yard? 

33.  A  man  gave  124y5^  acres  of  land  to  his  two  sons,  giv- 
ing |  of  it  to  the  elder  and  |  to  the  younger.     How  many 
acres  did  each  receive  ? 

34.  If  it  requires  21|  days  for  a  man  to  dig  a  ditch,  in 
what  time  can  he  dig  |  of  it  ? 

DIVISION  OF   FRACTIONS 

166.  What  operations  upon  the  dividend  and  divisor  divide 
the  quotient  ? 

What  operations  on  the  numerator  and  denominator  divide 
the  value  of  the  fraction  ? 

l.    y9y  -7-  3  =  ?    What  is  the  easiest  way  to  divide  -^  by  3  ? 


2.    ^g  -r-  3  =  ?    What  is  the  easiest  way  to  divide  ^  by  3  ? 
-*-  3  =  T&*  =  &• 

167. 


Rule  for  Dividing  a  Fraction  by  an  Integer 

1.  Divide  the  numerator  or  multiply  the  denominator 
of  the  fraction  by  the  given  integer. 

2.  Reduce  the  result  to  its  simplest  form. 


162  PRIMARY   ARITHMETIC 


168 

.    Mental.     Divide  : 

3. 

I 

by  3 

7       16 
''      16 

by  5 

11. 

1  5 
21 

by 

8 

15. 

II 

by  5 

4. 

I 

by  3 

8.      1 

by  6 

12. 

^ 

by 

10 

16. 

I 

by  3 

5. 

l 

9 

by  4 

9.     f 

by  3 

13. 

41 

by 

8 

17. 

I5o 

by  4 

6. 

i 

by  4 

10.    I 

by  3 

14. 

A 

by 

7 

18. 

¥ 

by  4 

19. 

A 

man 

divides  $ 

|  equally 

am<*»ng 

4 

boys. 

What 

part 

of  a  dollar  does  each  receive  ? 

20.  A  boy  wishes  to  put  |  of  a  bushel  of  chestnuts  into  5 
bags.     How  much  will  each  bag  contain  ? 

21.  If  4  pounds  of  coffee  cost  $|,  what  will  one  pound 
cost? 

22.  Divide  $  |  equally  among  5  boys.     What  is  the  share 
of  each  ? 

23.  How  much  is  1  -=-  4  ?  \  divided  by  5  ?  1  divided  by  6  ? 


¥-bj3 
if  by  6 
ft  by  2 
ft  by  7 
II  by  12 
16.  Divide  14§  by  3. 

:  "3~  SOLUTION.  —  We  may  change  the 

"V"  ~*~  "3  =  ^  =  4-|  mixed  number  to  an  improper  frac- 

Qr  tion    and   divide   according  to  the 

o  rule,   or    we    may   divide    without 

)      "5"  changing  to  an  improper  fraction. 

4|  14|  -r-  3  =  4  with  a  remainder  of  2|. 


69.    Written.     Divide: 

1. 

if 

by 

5 

6. 

fl 

by 

7 

11. 

2. 

fl 

by 

6 

7. 

if 

by 

2 

12. 

3. 

1! 

by 

5 

8. 

ii 

by 

3 

13. 

4. 

13T 

by 

7 

9. 

ti 

by 

10 

14. 

5. 

¥ 

by 

4 

10. 

M 

by 

5 

15. 

DIVISION  OF   FRACTIONS  163 

Find  the  quotients  : 

17.  476      _g_  7         2CX    385|  +  5  =  ?       23<   264f      -*-  4  =  ? 

18.  384f    -g-  5         21.    16-|    -s-  5  =  ?       24.    9826-^  -  6  =  ? 

19.  .287^  -*-  8         22.    30f    -5-  7  =  ? 

25.  If  16  bushels  of  apples  cost  $8|,  what  will  1  bushel 
cost? 

26.  Five  heirs  shared  equally  in  the  division  of  a  legacy 
of  $35,862f  .     What  was  the  share  of  each  ? 


170. 


|  -r-  7  =  7  —  -  .    What  principle  is  applied  here  ?    We  have 

divided  |  by  7.  The  divisor  given  was  -^  ;  7  is  how  many 
times  as  large  as  -^  ?  Since  we  have  used  a  divisor  11  times 
as  large  as  the  given  divisor,  how  does  the  quotient  compare 
with  the  correct  quotient  ?  State  the  principle.  How  shall 
we  correct  the  quotient  ?  What  is  the  easiest  way  to 

multiply  7  —  -  by  11?    The  quotient  then  becomes  -z  --  •=-. 
o  x  7  o  x  7 

This   is   the    same    as    multiplying   |   by   what    fraction  ? 

I  x  ¥  =  ft-     Ans- 

What  do  you  do  with  ^-  to  get  -y~  ? 

2.    19^3  =  ?        19^-V-        -Y-^^=iIax¥  =  1F  = 
30|.    Ans. 

What  is  done  with  the  integer  before  dividing  ? 

7       32 
3     614  -*-  -1-  7-  =  ?  6lJr  -1-  li  —  ^  x  ^  —  ^4-  —  24^      J.TIS 

ul¥   '64""        ul^   *  et~~   tg        T7  ~      9  9*      -aiw. 

9 
What  is  done  with  the  mixed  number  before  dividing  ? 


164  PRIMARY   ARITHMETIC 

171.    The  above  examples  illustrate  the  following 


Rule  for  the  Division  of  a  Fraction  by  a  Fraction 

1.  Interchange  the  terms  of  the  divisor. 

2.  Multiply  the  dividend  by  the  divisor  with  terms 
inverted. 

3.  Express  integers  and  mixed  numbers  as  fractions 
before  dividing. 


172.    Example    1  may  be   solved  also  by  reducing  both 
dividend  and  divisor  to  a  common  denominator,  thus  : 

3       7       3x11       7x5 


5      11      5  x  11      11  x  5 

The  denominator  5  x  11  being  common  to  both  fractions, 
we  divide  the  numerator  of  the  dividend  by  the  numerator 
of  the  divisor,  thus, 

3x  11=33 

7x5      35' 

This  gives  the  same  result  as  multiplying  the  dividend  by 
the  divisor  with  terms  interchanged,  thus,  f  x  ^  =  ff . 

173.    Find  the  quotients  : 


4. 

*+! 

9. 

3  2  -*-  ii 

14. 

2-H| 

19. 

2f  + 

52 

5. 

tt-*f 

10. 

**i  ~"~  A 

15. 

^T7o 

20. 

7i- 

!| 

6. 

T5*-t 

11. 

_3_  _^_  51 
11    •    U4 

16. 

10-  f 

21. 

2|  + 

T5 

7. 

1  ft             O 

JLfi.  _s_  J. 

2Y     '    3 

12. 

i7?-4! 

17. 

f-i-14 

22. 

2i  + 

3J 

8. 

1A  _._  _T_ 
15    '     10 

13. 

tt  +  fi* 

18. 

M-8 

23. 

8i- 

9I 

*  DIVISION  OF   FRACTIONS  165 

24.    |  X  f  -*-  f  of  f  =  ? 

O  o  O  O 

SOLUTION.  —  Inverting  the  divisor,  indicating  the  operations,  and  can- 
celling, we  have 

£      3      6      ^3 


25.  f  Of  9  -f-f  Of  f  27.     3|  -r-  f  X  |  Of  2 

26.  |  Of  -If  -r-  f  Of  4  28.     f  X  f  X  f  -f-  71 

29.  Divide  3682  by  5J. 

SOLUTION.  —  When  the  dividend  contains  several  figures  and  the 
51^)3682  divisor  is  a  mixed  number,  it  is  often  more  convenient  to 
2  2  divide  as  above. 

TT  \  70^/1  ^e  multiply  both  dividend  and  divisor  by  2,  when 

the  divisor  becomes  11  (halves),  and  the  dividend  7364 
6^T5T   (halves).     Dividing,  the  quotient  is  669T5T. 

Find  the  quotients: 

30.  356-4J  33.  296  -v-  101  36.    76,582-91 

31.  728-81  34.  39,846  -r-3£          37.    28,769  -7f 

32.  397  -f-  51  35.  44,077  H-  51 

38.  There  are   51  yards  in  a  rod.     How  many  rods  in 
3158  yards  ? 

39.  If  a  man  walks  15^  miles  a  day,  in  how  many  days 
can  he  walk  155  miles  ? 

40.  What  is  the  price  of  coal  per  ton  when  16  tons  cost 

|73|? 

41.  How  much  does  a  man  earn  in  a  day  if  he  earns  f  84| 
in  a  month  of  26  days  ? 

42.  When  flour  is  |6|  per  barrel,  how  many  barrels  can 
be  bought  for  $297? 


166  PRIMARY  ARITHMETIC 

174.    A  fraction  that  has  a  fraction  in  either  or  both  of  its 
terms  is  a  Complex  Fraction.     Thus, 

A    JL    M    M         i    I  -s-9 
8f  16'  25'   7f  If  -| 

are  complex  fractions. 

A  fraction  whose  terms  are  integers  is  a  Simple  Fraction. 
Thus,  1J  is  a  simple  fraction. 

1.  Reduce  —  to  a  simple  fraction. 

7      73     ft9      7     26      7       3      21 
—  =  7  -f-  84  =  —  i  --  =  -  x  —  =  —  •.     Ans. 
8f  1      3      1      26     26 

JL 

2.  Reduce  1*  to  a  simple  fraction. 

i  =  —  -*-  40  -       ft       -  —      Ans 
40      17  '         ~17x£0~136' 

8 
7& 

3.  Reduce  _  i.  to  its  simplest  form. 


8    '  20~  ji      53 
2t 

175.    From  the  examples  we  may  obtain  the  following 


Rule  for  the  Reduction  of  a  Complex  Fraction  to  its 
Simplest  Form 

1.  Perform  the  operations  indicated  in  the  numera- 
tor, if  there  are  any. 

2.  Perform  the  operations  indicated  in  the  denomi- 
nator, if  there  are  any. 

3.  Divide  the  numerator  by  the  denominator,  and 
reduce  the  result  to  its  simplest  form. 


THE   THREE   QUESTIONS   OF   RELATION  167 

176.    Change  to  simple  fractions : 

A  9  fi  5  Q 


I  18 


13. 


1 


14.  If  |  of  an  acre  of  land  is  worth  $72^-,  what  is  the 
value  of  an  acre  at  the  same  rate  ? 

15.  There  are  5J  yards  in  a  rod.     How  many  rods  in  70-| 
yards  ? 

16.  At  $5J  a  ton,  how  many  tons  of  coal  can  be  bought 

for  8731? 

THE  THREE  QUESTIONS  OF  RELATION 

177.    1.    3  times  4  equals  what  ?     Am.  12. 

2.  12  is  how  many  times  4  ?     Ans.  3. 

3.  12  is  3  times  what  ?     Ans.  4. 

In  question  1,  we  have  two  factors,  to  find  their  product. 
In  questions  2  and  3,  we  have  the  product  and  one  factor,  to 
find  the  other  factor. 

1.  Form  questions  like  2  and  3  from  the  following  state- 
ment :  5  x  6  =  30. 

a.  i  of  8  equals  what  ? 

Multiplying  8  by  J,  we  have  4.     Ans. 

b.  4  is  \  of  what  ? 

Since  Jx8  =  4,  4-s-J=8.     Ans. 

c.  4  is  what  part  of  8  ? 

Since      x8  =  4,4-*-8  =    .     Ans. 


168  PRIMARY   ARITHMETIC 


Principle 

The  product  of  two  numbers  divided  by  one  of  them 
gives  the  other. 


To  THE  TEACHER.  —  In  such  examples  as  question  a,  after  the  prod- 
uct is  found,  it  may  be  used  with  each  of  the  two  numbers  to  form 
successively,  question  b  and  question  c.  Drill  upon  these  three  questions 
of  relation  should  be  so  thorough  that  each  question  will  suggest  its  own 
solution  instantly. 

2.  J  of  24  =  what  ?     (Question  a.) 

3.  After  finding  the  product  in  example  2,  form  question 
b.     Question  c. 

4.  8  is  J  of  what  ?     (Question  5.) 

SOLUTION.  —  From  the  question  it  is  evident  that  8  is  the  product  of 
two  numbers,  and  that  i  is  one  of  them.  Therefore,  8  -H  J  =  24.  8  is 
i  of  24. 

5.  What  part  of  24  is  8  ?     (Question  c.} 

SOLUTION. —  It  is  evident  that  8  is  the  product  of  two  numbers,  and 
24  is  one  of  them.  Therefore,  8  -  24  =  &  or  J.  8  is  J  of  24. 

Question  a 
Find  the  result,  and  form  questions  b  and  c : 

6.  How  much  is  f  of  12  ?  9.    f  of  15  =  ? 

7.  How  much  is  f  of  16  ?  10.    f  of  21  =  ? 

8.  How  much  is  4  of  20  ?  11.    4  of  40  =  ? 

O  O 

Question  b 
Find  the  result,  and  form  questions  a  and  c : 

12.  15  is  |  of  what  ?  15.    18  is  f  of  what  ? 

13.  4  is  f  of  what  ?  16.    24  is  f  of  what  ? 

14.  9  is  f  of  what  ?  17.    25  is  ^  of  what  ? 


THE   THREE   QUESTIONS   OF   RELATION  169 

Question  c 
Find  the  result,  and  form  questions  a  and  b : 

18.  What  part  of  24  is  8  ?          21.    21  is  what  part  of  35  ? 

19.  What  part  of  18  is  12  ?       22.    28  is  what  part  of  63  ? 

20.  What  part  of  9  is  2  ?  23.    15  is  what  part  of  25  ? 

Find  the  result,  form  the  other  two  questions,  and  solve 
each: 

24.  |  of  56  equals  what  ?          28.    How  much  is  fa  of  96  ? 

25.  What  part  of  49  is  14  ?       29.    38  is  T2T  of  what  number  ? 

26.  26  is  |  of  what  ?  30.    16  is  what  part  of  80  ? 

27.  65  is  what  part  of  120  ?       31.    1 8  is  -f$ of  what  number? 

REMARK.  —  Each  of  the  following  problems  contains  one  or  more  of 
the  three  questions  of  relation.  Before  attempting  to  solve  any  of  them, 
the  pupil  should  state  the  question  in  each  of  them. 

32.  James  had  56  marbles,  and  John  |  as  many.     How 
many  had  John  ? 

The  question  is,  How  much  is  |  of  56  ?  —  a. 

33.  John  had  42  marbles,  which  was  |  as  many  as  James 
had.     How  many  had  James  ? 

The  question  is,  42  is  f  of  what  ? —  b. 

34.  James  had  56  marbles,  and  John  42.     John's  marbles 
are  what  part  of  James's  ? 

The  question  is,  What  part  of  56  is  42  ?  —  c. 

35.  A  man  sold  50  acres  of  land,  which  was  f  of  all  he 
had.     How  many  acres  had  he  at  first  ? 

36.  A  boy  had  20  cents  and  spent  15  cents.     What  part 
of  his  money  did  he  spend  ?     What  part  was  left  ? 

37.  Mr.  A  has  640  sheep,  and  Mr.  B  -^  as  many.     How 
many  has  Mr.  B? 


170  PRIMARY   ARITHMETIC 

ALIQUOT  PARTS 

178.    An  aliquot  part  of  a  number  is  any  integer  or  mixed 
number  that  is  exactly  contained  in  it. 

PARTS    OF    A    DOLLAR 

6J  cents  =  i^g  37-|  cents  =  $f 

81  cents  =  $  ^  50    cents  =  $  J 

12  1  cents  =  I  J  621  cents  =  f  £ 

16f  cents  =  $  J  66§  cents  =  $f 

25    cents  =  $|  75    cents  =$£ 

33J  cents  =  |  J  871  cents  =  if 

What  is  the  cost  of  33  books  at  16|  ^  each  ? 
33   books   cost  33  times  16f&  or  33  times 

$5.50. 


Oral.     Multiply  : 

1.  121  cents  by  16  7.  371  cents  by  8 

2.  16|  cents  by  12  8.  50    cents  by  15 

3.  25    cents  by  20  9.  621  cents  by  8 

4.  331  cents  by  27  10.  66|  cents  by  9 

5.  6J  cents  by  16  11.  75    cents  by  4 

6.  8J  cents  by  24  12.  871  cents  by  8 

13.    What  is  the  cost  of  : 


16  pounds  of  bacon  @  12|^  a  pound? 
16  balls  @  50^  each? 
36  yards  of  ribbon  @  331^  a  yard  ? 
36  pounds  of  candy  @  25^  a  pound? 
8  pounds  of  tea  @  621  ^  a  pound  ? 

The  sign  @  means  at.     The  sign  ^  means  cents. 


ALIQUOT   PARTS  171 

Written. 

What  is  the  cost  of  : 

14.    66  pounds  of  pork  at  12^  cents  a  pound? 

48  pounds  of  veal  at  16|  cents  a  pound? 

65  boxes  of  strawberries  at  25  cents  a  box? 

15  yards  of  flannel  at  831  cents  a  yard? 

80  pounds  of  honey  at  25  cents  a  pound? 

48  pounds  of  tea  at  50  cents  a  pound? 

179.  l.    At  25^  a  pound,  how  many  pounds  of  butter  can 
be  bought  for  $8? 

As  many  pounds  as  25^  or  $^  is  contained  times  in  $8. 
$8  -s-  $|  =  32  pounds.     Ans. 

Oral.     Divide : 

2.  $3  by  33|^        6.    $lby6|^  9.    $4  by  12J* 

3.  |5  by  25^  7.    $10  by  50^          10.    $2  by 

4.  $2  by  8$ ft          8.    16  by  331^          11.    $3  by 

5.  $9  by  12^ 

180.  Written.  t 

12.  At  25  cents  apiece,  how  many  hats  can  be  bought  for 
$6? 

13.  At  25  cents  a  pound,  how  many  pounds  of  cheese  can 
be  bought  for  $  5  ? 

14.  At  16|  cents  a  dozen,  how  many  dozen  eggs  can  be 
bought  for  $4? 

15.  How  many  pounds  of  beef  can  be  bought  for  $4  at 
$.16|  a  pound ? 

16.  At  33^  a  yard,  how  many  yards  of  linen  can  be 
bought  for  $10? 

17.  How  many  penknives  can  be  bought  for  $6  at  33| 
cents  apiece? 

18.  24x1.12-1  =  ?  19.    124  -1-$.  12J=? 


172  PRIMARY   ARITHMETIC 

REVIEW   OF   FRACTIONS 

181.     Oral. 

1.  Change  J  to  sixths.     To  ninths. 

2.  Change  J  to  sixths.     To  ninths. 

3.  Express  ^  in  larger  terms.     What  operations  did  you 
perform  ? 

Express  |  in  smaller  terms.     What  did  you  do  ? 

Change  the  following  : 

4.  I  to  lOths  6.   %  to  27ths  8.    4-  to  25ths 

o  «  •  « 

5.  |  to  9ths      7.  I  to  56ths     9.  f  to  84ths 

o  o  / 

Change  to  lowest  terms  : 

10.  f  12.    1|  14.    ff  16.    If 

11.  1§  13.     f$  15.     ||  17.    Jf 

18.  Reduce  5J  to  halves.     71  to  eighths.     4|  to  sixths. 
4|^  to  sevenths. 

19.  Change  41  to  9ths.     3|  to  3ds.     5T%  to  lOths.     8|  to 
5ths.     7-    to  llths. 


Reduce  to  improper  fractions  : 

20.  3f  22.     2|  24.     8^  26.     12| 

21.  41  23.     3  25.     9|  27. 


28.  How  many  dollars  in  $  -2/-  ?     in  $  !y4-  ?     in  $  -\8-  ? 

29.  12  fourths  of  a  bushel  are  equal  to  how  many  bushels? 
36  fourths  ?     40  fourths  ? 

30.  To  how  many  dollars  are  8  fourths  of  a  dollar  equal? 
9  fourths?     11  fourths? 

Reduce  to  integers  or  mixed  numbers  : 

31.  |  33.    £  35.     ^  37.     iU. 

32.  f  34.     %*•  36.     Af  38. 


REVIEW  OF   FRACTIONS  173 

39.  Change  ^  and  ^  so  both  may  have  20  for  a  denomi- 
nator. 

40.  Change  J,  J,  and  ^  each  to  12ths. 

41.  Change  f  and  |  each  to  24ths. 

42.  A  boy  paid  -|  of  a  dollar  for  a  book  and  ^  of  a  dollar 
for  a  paper.     How  much  did  he  pay? 

43.  John  saves  J  a  dollar  a  week,  and  Charles  f  of  a  dol- 
lar.    How  many  fourths  do  both  save  ? 

44.  Henry  gave  J  of  his  marbles  to  one  boy  and  f  of  them 
to  another.     How  many  twelfths  do  both  receive  ? 

45.  A  clerk  sold  J  a  pound  of  tea  to  one  customer,  -£  to 
another,  and  |  to  another.     How  many  eighths  did  he  sell? 

46.  A  man  pays  ^  of  his  salary  for  rent,  ^  for  table  ex- 
penses, and  T2Q-  for  clothing.     What  part  of  his 'money  was 
expended  for  rent,  table,  and  clothing? 

47.  A  boy  had  $T9^  and  spent  f  J.     What  part  of  a  dollar 
had  he  left? 

48.  A  owns  |  of  a  store,  and  B  ^.    How  much  of  the  store 
does  A  own  more  than  B  ? 

49.  John  runs  J  of  a  mile,  and  Jerry  f  of  a  mile.     Which 
runs  farther,  and  what  part  of  a  mile  ? 

50.  Mr.  Ames  owned  ^  of  a  farm  and  sold  ^  of  it.     What 
part  remained? 

51.  What  is  the  difference  between  f  of  anything  and  -| 
of  it  ?     Which  is  greater  ? 

52.  Lucy  has  $-|,  and  Alice  $|.     Which  has  the   more, 
and  how  much  ? 

53.  How  much  is  J  of  J  of   an  orange?     ^  of   ^  of   an 
orange  ? 

54.  At  $ -|  each,  what  will  8  books  cost? 


174  PRIMARY   ARITHMETIC 

182.   Written. 

1.  Find  the  cost  of  four  pieces  of  cloth,  measuring  231 
yards,  25f  yards,  22|  yards,  and  21|  yards,  at  $  2  a  yard. 

2.  Charles  has  $  15|  in  the  bank.     How  much  more  must 
he  earn  before  he  has  $50? 

3.  From  the  sum  of  2|  and  31 J,  take  the  difference  of  5| 
and  41.      (Indicate.) 

4.  Which  is  greater,  the  product  of  |  and  1,  or  the  dif- 
ference ?     How  much  ? 

5.  A  man  drew  from  the  bank  $68,  which  was  |  of  his 
entire  deposit.     How  much  had  he  at  first?     (Question.) 

6.  A  sum  of  money  was  divided  between  John  and  James. 
John  received  |-  of   it,  and  James   $300.     How   much  did 
John  receive? 

7.  A  merchant  paid  $272  for  flour  at  $|  a  barrel.     How 
many  barrels  did  he  buy  ? 

8.  Subtract  2  from  both  terms  of  the  fraction  |.     Do  you 
increase  or  diminish  the  fraction,  and  how  much  ?     Add  2  to 
each  term  and  find  the  difference. 

9.  What  must  be  added  to  |  +  If  +  l  to  make  5  ? 

10.  What  number  multiplied  by  25J  will  make  264  ? 

11.  A  lady  gave  $|  for  ribbon,  $  1  for  pins,  $|  for  velvet, 
and  $^-  for  lining.*    What  change  did  she  receive  from  a  five- 
dollar  bill? 

12.  What  will  4|  pounds  of  raisins  cost  at  15^  a  pound? 

13.  From  25  yards  of  cloth,  a  tailor  used   If  yards  for 
making  a  vest,  21  yards  for  a  pair  of  pantaloons,  3J  yards 
for  a  coat,  and  4^  yards  for  an  overcoat.     How  much  cloth 
was  left? 


REVIEW   OF   FRACTIONS  175 

14.  I  owned  |-  of  a  farm  and  sold  ^  of  my  share.     What 
part  of  the  farm  did  I  sell,  and  what  part  did  I  retain  ? 

15.  Henry  had  $78  in  the  bank.     He  withdrew  $15  at  one 
time  and  $38  at  another  time.     What  part  of  his  money  did 
he  withdraw?     (Question.)    What  part  remained?     (Ques- 
tion.) 

16.  A  man  having  150  sheep  sold  ^  of  them  and  kept  the 
remainder.     How  many  were  sold  ?     How  many  were  kept  ? 

17.  A   man  owning  -|  of  a  factory  sold  J  of  his  share. 
What  part  of  the  factory  did  he  sell? 

18.  A  man  sold  50  sheep,  which  was  |  of  his  whole  flock. 
How  many  sheep  had  he  at  first? 

19.  If  4  yards  of  ribbon  cost  35 1^,  what  is  the  price  per 
yard  ? 

20.  If  20^  pounds  of  sugar  cost  80  cents,  what  will  50 
pounds  cost?     (Use  cancellation.) 

21.  If  20|^  pounds  of  sugar  cost  83^,  how  many  pounds 
can  be  bought  for  $2.00  ? 

22.  I  bought  55  yards  of  cloth  at  $|-  a  yard,  and  sold  it 
at  $-|  a  yard.     What  was  the  profit? 

23.  If  an  acre  of  land  is  worth  $150,  what  part  of  an  acre 
will  $  50  buy  ? 

24.  How  long  will  it  take  a  boy  to  pay  for  a  $  75  bicycle, 
if  he  can  pay  $-|  a  day? 

25.  -|  of  a  class  are  boys  ;  there  are  30  girls.     How  many 
pupils  in  the  class  ? 

26.  If  2J  pounds  of  tea   cost  $1.00,  how  much  will   3| 
pounds  cost  ? 

27.  At  $^  a  pound,  what  is  the  cost  of  |  pound  of  tea  ? 

28.  Find  the  product  of  f ,  |-,  5|,  and  2^.    » 


DECIMAL  FRACTIONS 


183.  A    Common    Fraction    is    generally    expressed    by 
placing  the  denominator  below  the  numerator. 

184.  A    Decimal    Fraction   has    a   denominator,    but   the 
latter  is  not  generally  written. 

The  denominator  of  a  common  fraction  may  be  any 
number. 

185.  The  denominator  of  a  decimal  fraction  must  be  10, 
or  100,  or  1000,  etc. 

NOTE.  —  The  word  decimal  comes  from  the  Latin  word  decem,  ten, 
and  so  the  denominator  of  every  decimal  fraction  is  10,  or  10  x  10, 
or  10  x  10  x  10,  etc. 

186.  A  Decimal  Fraction,  or  Decimal,  is  a  fraction  whose 
unit  is  divided  into  tenths,  hundredths,  thousandths,  etc. 

187.  A  Decimal  is  always  written  at  the  right  of  a  period 
(.),  called  the  Decimal  Point. 

We  use  the  decimal  point  in  writing  U.S.  money  to  sepa- 
rate the  dollars  from  the  cents  and  mills.  5  dollars  and 
28  cents  is  written  $5.28.  But  28  cents  is  T2^  of  a  dollar; 
hundredths  therefore  are  written  like  cents,  with  twc  decimal 
figures. 

NOTE.  —  Any  figure  at  the  right  of  the  decimal  point  is  a  decimal 
figure. 

176 


DECIMAL   FRACTIONS  177 

Tenths  are  written  like  dimes,  with  one  decimal  figure. 

Hundredths  are  written  with  two  decimal  figures,  -f-^  — 
•28;  y3^-=.39;  y|-Q  =  . 06. 

Thousandths  are  written  with  three  decimal  figures, 
=  .325;  ^=.864;  Tffo=.025. 

Name  the  denominators : 

1.  .6  3.    .105  5.    .05 

2.  .17  4.    .006  6.    .225 

188.    Change  to  the  decimal  form  : 

!•      ~^\  6'      -8— oV  H'      Hfo^O  ^.      -9?f 

2      _8JL  7      _4JL  12      -1— 1-  17      -1— 

100  100  100  10 

3>     T8OW  8'     1\  13'     T"00"  18* 


4-.T60  9-     Tto  14-     foOT  19' 

5-    iVo          10-    iMo         15-    I5o°o  20- 

189.  Change  to  common  fractions,  and  read  : 

21.  .36  26.    .485  31.   5.6 

22.  .7  27.    .016  32.    5.06 

23.  .125  28.     .16  33.    5.006 

24.  12.2  29.     .06  34.    5.600 

25.  6.25  30.    .6  35.    5.060 

190.  Write,  first  as  common  fractions,  then  as  decimals : 

36.  Four  tenths. 

37.  Seventy-five  hundredths. 

38.  One  hundred  twenty-five  thousandths. 

39.  Sixteen,  and  forty-eight  hundredths. 

40.  Twelve,  and  four  tenths. 


178  PRIMARY  ARITHMETIC 

41.  Six  tenths. 

42.  Six  hundredths. 

43.  Six  thousandths. 

44.  How  many  decimal  figures  are  required  to  express 
thousandths  ?     Hundredths  ?     Tenths  ? 

45.  Read  the  numerators  only  in  examples  36  to  43. 
Write  the  following  as  decimals,  and  read  the  numerator 

of  each,  then  the  denominator  of  each : 

46.  Two  hundred  eighty-two  thousandths. 

47.  Fifty-six  hundredths. 

48.  Seven  tenths. 

49.  Six  hundred  thousandths. 

191.   Oral. 

1.  What  part  of  10  units  is  1  unit  ? 

2.  What  part  of  1  ten  is  1  unit  ? 

3.  What  part  of  2  hundreds  is  2  tens  ? 

4.  In  the  number  555,  what  is  the  value  of  the  first  5  at 
the  right  ?     The  second  5  ?     The  third  5  ? 

5.  Upon  what  does  the  value  of  any  figure  depend  ? 

6.  The  value  of  the  first  five  is  what  part  of  the  value 
of  the  second  five  ? 

7.  -f^  is  what  part  of  2  units  ? 

8.  In  the  number  5.5,  tne  value  of  the  right-hand  5  is 
what  part  of  the  value  of  the.  left-hand  5  ? 

9.  Write  five  and  five-tenths  decimally. 

10.  .5  is  what  part  of  5? 

11.  In  the  decimal  .555,  what  is  the  value  of  the  first  o 
to  the  right  ?     The  second  5  ?     The  third  5  ? 

12.  How  much  greater  is  the  value  of  the   third  5  than 
the  second  5  ? 


DECIMAL   FRACTIONS  179 

13.  How  much  greater  is  the  second  5  than  the  first  5  ? 
In  the  number  555.555,  we  have  found  that  the  value  of 

each  5  is  -^  as  much  as  the  next  5  to  the  left.  Also  that 
the  value  of  any  5  is  10  times  as  great  as  the  value  of  the 
next  5  to  the  right. 

In  decimals  as  in  integers,  any  figure  removed  one  place 
to  the  right  is  diminished  tenfold,  and  when  removed  one 
place  to  the  left  is  increased  tenfold. 

14.  In  the  number  32.6,  what  would  be  the  value  of  the 
2  if  it  were  removed  one  place  to  the  right  ?     One  place  to 
the  left  ? 

Read:  15.    .222  17.    22.2 

16.    2.22  18.    222. 

192.  Integers  and  Decimals. 


03 

•§  £ 

§  .  S    § 

02        02  +J        M 

2      Id  .        09  1?        2 

r^     08       .  02     H  ?j    *^ 

Ho203                       •  ^3-M  OlHw 

i  •    0    «O              M  -^TS  d    JL     9 

§   in   !;,.  in  ill 

i— i           flpQ          ^o^  s3^o  fl    ^   r"i 

§        WHH        WHO  HWH  HffiS 

4,       243,       684  .      268,  504 

The  number  is  read  4  million,  243  thousand,  684  and  268 
thousand  504  millionths. 
193. 


Rule  for  Reading  Decimals 

1.  For  the  numerator,  read  the  decimal  as  an  integer. 

2.  For   the    denominator,   give    the   place    name    of 
the  last  figure. 


NOTE.  —  The  denominator  of  a  decimal  is  always  named,  but  seldom 
written. 


180  PRIMARY   ARITHMETIC 

In  reading  an  integer  and  a  decimal,  read  "  and  "  where 
the  decimal  point  occurs. 

What  is  the  denominator  when  the  decimal  has  one  figure  ? 
Two  figures  ?  Three  figures  ?  Four  figures  ?  Five  figures  ? 
Six  figures  ?  Seven  figures  ? 


194 

,  Read: 

1. 

.368 

7. 

28.3005 

13. 

.4983695 

2. 

.894 

8. 

.28962 

14. 

4.98369 

3. 

.5328 

9. 

15.60534 

15. 

49.8369 

4. 

.2053 

10. 

37.00537 

16. 

498.369 

5. 

25.623 

11. 

25.203602 

17. 

.000400 

6. 

7.0063 

12. 

38.000006 

18. 

.0004 

19.  In  example  11  remove  the  point  two  places  to  the 
right,  and  read.     Four  places  to  the  right.     One  place  to 
the  left. 

20.  Read  the  denominators  only  in  the  last  five  examples. 
195. 


Rule  for  Writing  Decimals 

Write  the  numerator,  prefix  naughts  when  necessary  to 
express  the  denominator,  and  place  the  point  at  the  left. 


How  many  decimal  figures  are  required  to  express  tenths  ? 
Hundredths?  Thousandths?  Ten-thousandths?  Hundred- 
thousandths  ?  Millionths  ?  Ten-millionths  ? 


.       WRITING   DECIMALS  181 

196.  Write  decimally : 

1.  Eight  tenths. 

2.  29  hundredths. 

3.  Sixteen,  and  284  thousandths. 

4.  4584  ten-thousandths. 

5.  Twenty-five  hundredths. 

6.  Twenty-five  thousandths. 

7.  Twenty-five  ten-thousandths. 

8.  Twenty-five  hundred-thousandths. 

9.  Twenty-five  millionth*. 

10.  1650,  and  464  thousandths. 

11.  One  thousand  one,  and  36  hundred-thousandths. 

12.  Sixteen,  and  six  thousandths. 

13.  Seven  hundred  eighty-four  millionths. 

14.  Twelve  hundred-thousandths. 

15.  Seventy -five  ten-thousandths. 

197.  Oral. 

1.  In  the  three  decimals,  .4,  .40,  .400,  is  there  any  differ- 
ence in  value  ? 

2.  What  is  the  effect  when  a  cipher  is  annexed  to  a 
decimal  ? 

3.  What  is  the  effect  when  a  cipher  is  annexed  to  an  inte- 
ger ?     Give  an  example. 

4.  In  the  decimals,  .4,  .04,  .004,  is  there  any  difference  in 
value  ? 

5.  What  is  the  effect  when  a  cipher  is  prefixed  to  a  deci- 
mal ?     Two  ciphers  ?     Give  examples. 

6.  What  is  the  effect  when  a  cipher  is  prefixed  to  an 
integer  ? 


182  PRIMARY  ARITHMETIC 

198. 


Principles 

1.  Ciphers  annexed  to  decimals  do  not  change  their 
values. 

2.  For  each  cipher  prefixed  to  a  decimal  the  value 
is  diminished  tenfold. 

3.  The  denominator  of  a  decimal  when  expressed  is 
always  1  with  as  many  ciphers  as  there  are  places  in 
the  decimal. 


REDUCTION  OF  DECIMALS 

199.  Decimals  may  be  reduced  to  a  common  denominator 
by  annexing  ciphers  sufficient  to  give  the  same  number  of 
decimal  figures  to  all  the  decimals. 

200.  Reduce  to  a  common  denominator  : 

1.  .5,  .365,  and  .4689. 

2.  .18963,  .5,  7.84,  .16005. 

3.  .28,  3.5,  .00005,  .256. 

4.  .5,  .05,  .005,  .0005,  .00005. 

5.  .0463,  .03,  .1,  .100010. 

6.  .38,  1.16,  .4,  78.592. 

201.  1.    Reduce  .375  to  a  common  fraction. 
SOLUTION.  —  .375  as  a  common  fraction  is  T3oW    -375  = 


Rule  for  reducing  Decimals  to  Common  Fractions 

Write  the   numerator,   omitting  the   decimal  point, 
supply  the  denominator,  and  reduce  to  lowest  terms. 


REDUCTION  OF  DECIMALS 


183 


Reduce  to  common  fractions  : 


2. 

.25 

8. 

.125 

14. 

.368 

3. 

.35 

9. 

.875 

15. 

16.75 

4. 

.75 

10. 

.375 

16. 

.00125 

5. 

.64 

11. 

.455 

17. 

.054 

6. 

.52 

12. 

.025 

18. 

.0250 

7. 

.38 

13. 

.561 

19. 

.01375 

20.    Reduce  .37|  to  a  common  fraction. 


100      100      200      8 

202.    Reduce  to  common  fractions 
21.    .121  24.    .181 

25.     .03| 


22.  .62| 

23.  .06^ 


26.     .25f 


27.     .871 


28. 
29. 


.66| 
.36| 


Reduce  to  mixed  numbers  : 
so.    16.25,  2.331,  34.75. 

203.    Reduce  |  to  a  decimal. 

|  =  3  times  ^.     3  =  (3.0)  30  tenths. 

^  of  3.0  =  (.7)  7  tenths  and  2  tenths  remainder. 

2  tenths  =  20  hundredths. 

Hence  f  =.7 +  .05  =  .75. 


Jof  .20  =  .05. 


Rule  for  reducing  Common  Fractions  to  Decimals 

Annex  decimal  ciphers  to  the  numerator,  and  divide 
by  the  denominator.  Point  off  in  the  quotient  as  many 
decimal  places  as  there  are  ciphers  annexed. 


184  PRIMARY  ARITHMETIC 

The  division  will  not  always  be  exact.  In  such  cases, 
write  the  remainder  over  the  divisor  as  a  common  fraction, 
or  place  the  sign  (  +  )  after  the  decimal  to  show  that  the 
result  is  incomplete. 

Thus,  |=.142f,  or  .142+. 

204.    Reduce  to  decimals  : 


2.    |  6.     f 

3-    i  7.    f 

4.    I  8.    f 


205.  ADDITION 

Add:  .35,4.375,  28.3065. 

.35 
4.375 

28.3065 


9-  tt 

13.    | 

17. 

10.  M 

14'    ft 

18. 

11.  if 

15.     3^ 

19. 

12.    -5-^ 

16.    | 

20. 

Rule  for  Addition  of  Decimals 

Write  the  numbers  so  that  the  decimal  points  stand 
in  a  column.  Add  as  in  integers,  and  place  the  point 
in  the  sum  directly  under  the  points  above. 


Add:    2.    3.25  3.    4.5  4.        .004 

7.163         .168        4.1 
15.0032       2.12        16.1563 

5.  .175  +  1.754-17.5  +  175. 

6.  145  +  14.5 +  1.45 +  .145  + .0145. 

7.  3.2 +  14.0063 +  .006  + 25.384 +  .1. 


SUBTRACTION  OF  DECIMALS  185 

8.  .8 +  .446 +  59.3 +  2.575  + 1.0056 +  .3. 

9.  1.45  +  2.365  +  96  +  .96  +  15.863  +  4.3  +  .0004. 

10.  446  +  44.6  +  37562  +  9  +  .8  +  .321  +  .16. 

11.  21.0005  +  .3842  +  .1  +  .005  +  3.6  +  .158. 

12.  1.0006  -J-  2001.1  +  .003  +  5.5  +  11.1111. 

206.  SUBTRACTION 


Rule  for  Subtraction  of  Decimals 

Write  the  numbers  so  that  the  decimal  point  of  the 
subtrahend  stands  directly  under  the  decimal  point  of 
the  minuend,  subtract  as  in  integers,  and  place  the 
point  directly  under  the  points  above. 


.  —  It  is  sometimes  convenient  to  give  the  decimals   the   same 
denominator,  by  annexing  decimal  ciphers. 

Subtract : 

1.   24.3  2.    2.86  3.   4.  4.    2.46 

4.5  1.325  1.15  .005 

Find  the  remainders : 

5.  7 -.15  10.  29.325-15.14 

6.  1-.004  11.  3.852 -.125 

7.  13-2.1  12.  1.1111 -.0011 

8.  3.256-1.05  13.  500 -.05 

9.  256.1-1.256  14.  25.3894-15.005 

15.    From  twenty-eight,  and  twenty-five  thousandths  take 
fourteen,  and  twenty-five  hundredths. 


186  PRIMARY   ARITHMETIC 

16.  From  one  tenth  take  one  thousandth. 

17.  Which    is    the    greater,    fifty    thousandths    or    five 
hundredths  ? 

18.  Take  one  thousandth  from  one  thousand. 

19.  From  5  hundred  take  5  hundredths. 

MULTIPLICATION 
207.   Oral. 

How  much  is  2  times  .3  ?     3  times  .3  ?     4  times  .3  ? 
7  times  .02  =  ?     12  times  .06  =  ?     12  times  $.12  =? 

iV  x  iV  =100  5  1  x.l  =  .01. 

'  .3  x.  05  =  .015. 
.3x.3=.09. 


T3^  =  YO-§-Q         How  many  ciphers  in  the  denominator 

of  the  product? 

How  many  ciphers  in  the  denominators  of  both  factors  ? 
Every  decimal  has  a  corresponding  common  fraction,  and 
for  each  cipher  in  the  denominator  of  the  common  fraction 
there  is  a  decimal  figure  in  the  decimal. 

How  many  decimal   figures  in   both 
•05  x.  3  =  ,015      factors? 


Rule  for  Multiplication  of  Decimals 

Multiply  as  in  integers,  and  point  off  from  the  right 
of  the  product  as  many  decimal  figures  as  there  are 
decimal  figures  in  both  factors. 


NOTE.  —  If  there  are  not  figures  enough,  prefix  ciphers. 


MULTIPLICATION   OF   DECIMALS  187 

Ciphers  at  the  right  of  a  decimal  have  no  value,  and  may 
be  omitted. 

2.8  1.25  .005  25 

x8  .6  .03  .06 

22.4  .750  .00015  L50 

Find  the  products: 

1.  .18  x.15  8.  13.3  xl.3 

2.  1.0005  x  .2  9.  100  x  .01 

3.  2.5  x  .06  10.  100.56  x  .0005 

4.  56  x  .005  11.  25.32  x  1.05 

5.  .005  x  1.6  12.  2.84  x  2| 

6.  25.05  xl.15  is.  "3.28  x  12£ 

7.  2.863  x  100  14.  1.111  x  1000 

208.    1.  Multiply  1.265  by  100. 

1.265 

100 
126.500 


To  Multiply  by  10,  100,  1000,  etc. 

Remove  the  decimal  point  one  place  to  the  right  for 
every  naught  in  the  multiplier. 
Do  not  write  the  multiplier. 


Oral.    Multiply: 

2.  3.84  by  10  7.  .3  by  100 

3.  12.63  by  100  8.  1.869  by  100 

4.  1.5555  by  1000  9.  32.856  by  1000 

5.  1.358  by  10  10.  138.56  by  1000 

6.  .25  by  1000  11.  11.11  by  100 


188  PRIMARY   ARITHMETIC 

DIVISION 

209.    Since  in  multiplication  there"  are  as  many  decimal 
figures  in  the  product  as  in  both  factors,  in  division  the  quo- 
tient will  have  as  many  decimal  figures  as  the  number  of 
decimal  figures  in  the  dividend  exceeds  those  in  the  divisor. 
^  19  A«5         Since  there  are  three  decimal  figures  in  the 
— ^7~^     dividend  and  one  in  the  divisor,  there  must  be 
two   in   the  quotient.       Prove   by   multiplying 
dividend  by  quotient. 
Divide  399.552  by  192. 

2.081 

192)  399.552 
384 
1555 
1536 
192 
192 


Rule  for  Division  of  Decimals 

In  all  cases  divide  as  in  integers,  then  place  the  deci- 
mal point. 

When  the  divisor  is  an  integer,  place  the  point  in  the 
quotient  directly  over  the  point  in  the  dividend,  in  long 
division  (directly  under  in  short  division). 

Prove  by  multiplying  the  divisor  by  the  quotient. 

When  the  divisor  contains  decimal  figures,  move  the 
point  in  both  divisor  and  dividend  as  many  places  to 
the  right  as  there  are  decimal  figures  in  the  divisor, 
then  place  the  point  in  the  quotient  as  if  the  divisor 
were  an  integer. 


DIVISION   OF   DECIMALS  189 

NOTE  1.  —  The  new  point  in  both  dividend  and  divisor  may  be  placed 
on  a  line  with  the  tops  of  the  figures,  and  the  original  point  may  stand, 
to  preserve  the  reading  of  the  decimals. 

NOTE  2.  —  In  the  above  example,  the  moving  of  the  point  two  places 
to  the  right  in  both  dividend  and  divisor  is  equivalent  to  multiplying 
each  by  100. 

NOTE  3.  —  If  the  quotient  does  not  have  a  sufficient  number  of  figures, 
prefix  ciphers. 

NOTE  4.  —  Before  commencing  to  divide  see  that  there  are  at  least  as 
many  decimal  places  in  the  dividend  as  in  the  divisor. 

NOTE  5.  —  If  there  is  a  remainder,  after  all  the  figures  of  the  dividend 
are  used,  annex  decimal  ciphers  and  continue  the  division. 

NOTE  6.  —  It  is  not  usually  necessary  to  have  "more  than  four  decimal 
figures  in  the  quotient. 

Divide  28.78884  by  1.25. 

23.031  + 
1.25*)28.78'884 
250 
378 
375 
388 
375 
134 
125 
9 

Divide  .125  by  .5. 
Divide  1.25  by  .5. 
Divide  12.5  by  .5. 

Divide  at  sight : 

1.  3)3.33  4.  .03). 333  7.  .5)25 

2.  3). 333  5.  .003). 333  8.  .05). 25 

3.  .03)333  6.  5)2.5  9.  .07). 28 


190 


PRIMARY   ARITHMETIC 


Find  quotients  and  prove  : 

210.    10.    3. 57  -.7 
.488  -s-.12 
16.55 -f-. 05 
13.13 -1.3 
1.111 -.01 
5555^.5 
.875  -5- .05 
73.5-1.05 


11. 

12. 
13. 
14. 
15. 
16. 
17. 
Divide : 

26.  Twenty-five  ten-thousandths  by  25  hundred ths. 

27.  4678  hundred-thousandths  by  9  ten-thousandths. 

28.  3582  ten-thousandths  by  3  hundredths. 


18. 
19. 
20. 
21. 
22. 
23. 
24. 
25. 

376  -.6 
376  -.06 
37.6  -.6 
3.76  -.06 
1.875  -.005 
15.55  -s-  .1 
l-.l 
.1-1 

To  divide  by  10,  100,  1000,  etc. 

Remove  the  decimal  point  one  place  to 
each  cipher  in  the  divisor. 

the  left  for 

Divide  at  sight  : 

29.     10)365.8              33. 

100)189.36           37. 

1000)1698.45 

30.     10)5                        34. 

100).  189               38. 

1000)1.111 

31.    10)148.963       35. 

100)148.369         39. 

1000)2948.36 

32.     10)115.55           36. 

100)4.983             40. 

1000)39.85 

Read  and  add  : 

i.    32.065 

2.        36 

.9486 

6.006 

2583 

.04 

4.25 

4 

.9602 

.032 

15 

.15 

.25 

100 

.001 

25.01 

56 

.56 

111.11 

141 

.141 

REVIEW   OF   DECIMALS  191 

REVIEW   OF   DECIMALS 

211.     l.    Tell  where  to   place   the   decimal  point  in  any 
product. 

2.  In  any  quotient. 

3.  In  any  remainder. 

4.  In  any  sum. 

5.  From  1  take  1  millionth. 

6.  Add  1  tenth,  1  hundredth,  and  1  thousandth. 

7.  Find  the  product  of  1  multiplied  by  .15. 

8.  Multiply  at  sight :  36.984  by  1000. 

9.  Divide  at  sight  :  159.83  by  1000. 

Change  to  decimals  : 

10.  |,  f  |,  16|,  25f 

Change  to  common  fractions  : 

11.  .28,  .38,  .375,  15.125. 

12.  If  John  earns  $8  in  a  week,  how  much  can  he  earn 
in  7.5  weeks? 

13.  If  a  barrel  of  flour  costs  $ 5.25,  how  many  barrels  can 
be  bought  for  $  105  ? 

14.  What  is  the  effect  when  a  decimal  figure  is  removed 
one  place  to  the  left  ?     To  the  right  ? 

15.  What  is  the  effect  when  an  integral  figure  is  removed 
one  place  to  the  left?     One  place  to  the  right? 

16.  At  15^  a  peck,  how  many  pecks  of  pop-corn  can  be 
bought  for  $3.75? 

17.  What  is  the   cost  of  28.78   yards  of  cloth  at  $  3.15  a 
yard? 


BILLS   AND    ACCOUNTS 


212.  An  Account  is  a  record  of  indebtedness  for  articles 
bought  or  sold,  cash  paid  or  received,  or  services  rendered. 

213.  A  Debtor  is  a  person  who  owes  a  debt. 

214.  A  Creditor  is  a  person  to  whom  a  debt  is  owed. 

215.  A  Bill  is  a  written  statement  of  a  debtor's  account, 
made  by  the  creditor. 

216.  A   Receipt  is  a  creditor's  written   acknowledgment 
that  he  has  received  payment  of  part  or  all  of  a  debt. 

217.  A  bill  is  Receipted  when  its  payment  is  acknowledged 
in  writing,  by  the  creditor,  or  b}^  some  authorized  person. 

NOTE. —  The  sign  @  is  for  at,  Dr.  is  for  debtor,  and  Cr.  for  creditor. 

1.  BILL   FORMS 

DETROIT,  MICH.,  July  1,  1901. 
JAMES  P.  BARNES, 

Bought  of  DEY  BROS.  &  Co. 


50  yards  Brussels  Carpet     @  $  1  15 

24     "      Oilcloth                   "  35 

4  dozen  pair  Merino  Hose  "  3  50 

2  Willow  Chairs                  "  4  50 


BILLS   AND   ACCOUNTS 


193 


2. 


JEROME  A.  PHELPS, 


FORM   OF    A    RECEIPTED    BILL 

NEW  YORK,  June  30,  1902. 

In  account  with  D.  0.  POTTER  &  Co. 


May 

u 

12  barrels  Flour                 @ 

$  6.50 

ft 
f 

(t 

14 

6  tubsButter,684pounds  " 

.24 

June 

10 

5  barrels  beef                    " 

25.28 

a 

25 

450  pounds  Ham                  " 

.09% 

Received  payment, 

D.  O.  POTTER  &  Co. 


3. 


Mr.  John  Q.  Adams  buys  of  D.  McCarthy  &  Co. : 

4  pounds  of  coffee  at  27  cents  a  pound. 
18  pounds  of  sugar  at  5J  cents  a  pound. 
•  5  gallons  of  molasses  at  60  cents  a  gallon. 
16  pounds  of  rice  at  8^  cents  a  pound. 
Make  out  the  bill. 

4.  James  Smith,  farmer,  sold  Richard  Dunn,  grocer,  the 
following  :    6  barrels  of  potatoes  at  11.80  a  barrel. 

2  tons  of  hay  at  $16  a  ton. 

3  cords  of  wood  at  $4  a  cord. 

360  pounds  of  butter  at  241  ^  a  pound. 
Make  a  receipted  bill. 

5.  Syracuse,  Dec.  5,  1898.      Edward  Smith,  sold  B.  M. 
Watson  65  yards  of  Brussels  carpet  at  $1.25  ;  24  yards  of  oil- 
cloth @  35^;  one  dozen  pair  of  merino  hose  @  $3.50;  2  willow 
chairs  @  $4.50.     Make  a  bill,  find  the  footing,  and  properly 
receipt  it. 

6.  Make  out  a  bill  of  groceries.     Foot  it,  and  receipt  it, 
with  F.  H.  Mead  as  creditor  and  Wm.  H.  Scott  as  debtor. 

T 

th" 


To  THE  TEACHER.  —  See  that  the  prevailing  prices  are  used,  and  that 
the  quantities  are  consistent. 


DENOMINATE   NUMBERS 


218.  A  number  composed  of  units  which  belong  to  a  table 
of  weights  or  measures  is  a  Denominate  Number.    Thus,  2  feet, 
7  gallons,  3  hours,  are  denominate  numbers. 

219.  A  number  composed  of  two  or  more  kinds  of  units 
belonging  to  the  same  table  is  a  Compound  Number.     Thus, 
2  yards,  1  foot,  6  inches,  and  1  ton,  50  pounds,  11  ounces, 
are  compound  numbers. 

LINEAR   MEASURES 

220.  Measures  used  in  measuring  distances  and  dimen- 
sions are  Linear  Measures. 

221.  The  Yard  is  the  standard  unit  of  linear  measure. 
With  a  yardstick  draw  a  line  one  yard  long.     Hold  your 

hands  one  yard  apart.  Name  objects  one  yard  apart.  How 
many  yards  apart  are  the  windows  of  your  schoolroom? 
Without  the  measure,  draw  a  line  one  yard  long.  Correct 
it.  Divide  it  into  3  equal  parts.  Each  part  is  one  foot  long. 

Hold  your  hands  one  foot  apart.  Measure  a  foot  on  your 
arm.  Name  objects  1  foot  long,  wide,  or  high. 

Draw  a  line  one  foot  long.  Correct  it  with  a  rule. 
Divide  it  into  12  equal  parts.  Each  part  is  1  inch.  Show 
how  long  1  inch  is.  Four  inches.  Six  inches. 

194 


DENOMINATE   NUMBERS  195 

With  a  yardstick,  measure  5|  yards  on  the  schoolroom 
floor.  This  is  1  rod.  How  many  feet  make  a  rod  ?  How 
many  rods  long  is  your  school  ground?  (Estimate  it.) 
How  wide  ?  Where  would  you  stop  if  you  should  walk  20 
rods  from  the  front  door  of  your  schoolhouse  ? 

320  rods  make  1  mile.  Name  some  places  1  mile  from 
your  school.  How  many  miles  do  you  walk  in  coming  to 
school  ?  How  many  yards  in  1  mile  ?  How  many  feet  ? 
How  many  inches  ? 

222.  The  answers  to  the  above  questions  give  us  the 
following 


TABLE    OF    LINEAR 

MEASURES 

12 

inches 

(in.)  make 

1 

foot 

(ft,). 

3 

feet 

make 

1 

yard 

(yd-)- 

PJ 

yards 

make 

1 

rod 

(rd.). 

320 

rods 

make 

1 

mile 

(mi.). 

5280 

feet 

make 

1 

mile. 

Oral. 

1.  How  many  inches  are  there  in  1  yd.  ? 

2.  How  many  inches  are  there  in  2  ft.  ?     3  ft.  ?     5  ft.  ? 

3.  How  many  feet  are  there  in  4  rd.  ?     2  rd.  ? 

4.  How  many  feet  are  there  in  5  yd.  ?     7  yd.  ?     11  yd.  ? 

5.  24  feet  are  how  many  yards  ? 

6.  How  many  feet  around  a  picture  2  ft.  long  and  1  ft. 
wide  ? 


196  PRIMARY   ARITHMETIC 

7.  How  many  inches  in  a  half  yard  ? 

8.  At  $.16  a  yard,  what  will  1^  yd.  of  ribbon  cost  ? 

9.  6  f t.  -f  2  ft.  -f-  4  ft.  are  how  many  yards  ? 

10.  How  many  feet  in  108  inches  ? 

11.  John  has  a  fish  pole  4  yd.  long.     How  many  inches 
long  is  it  ? 

12.  How  many  rods  in  5  miles  ?     7  miles  ?     1J  miles  ? 

13.  How  many  feet  in  ^  mile  ?     3  miles  ?     1^  miles  ? 

14.  Stepping  two  feet  at  a  step,  how  many  steps  will  be 
taken  in  walking  2  miles  ? 

SURFACE  MEASURES 

223.  A  Surface  is  that  which  has  only  length  and  breadth. 
Thus,  the  top  of  a  desk,  the  outside  of  a  book,  the  upper  and 
under  sides  of  a  board,  are  surfaces. 

224.  An  Angle  is  the  difference  in  direction  of  two  lines 
that  meet.     Thus, 


225.  A  Plane  Surface  is  a  surface  which  would  be  touched 
by  all  the  points  of  a  straight  line  drawn  in  any  direction 
upon  it.     Thus,  the  top  of  a  table  is  a  plane  surface. 

226.  A   Plane   Figure    is   a   portion   of   a   plane   surface 
bounded  by  lines.     Thus,  a  triangle,  an  oblong,  a  circle,  are 
plane  figures. 


SURFACE   MEASUREMENTS 


197 


One 
square 

inch 


227.  A  Square  is  a  plane  figure  bounded 
by  four  equal  straight  sides  and  having 
four  equal  angles. 

A  square  whose  side  is  one  inch  is  a 
Square  Inch.  Thus, 

A  square  whose  side  is  one  foot  is  a 
Square  Foot.  Draw  a  square  foot. 

A  square  whose  side  is  one  yard  is  a 
Square  Yard.  Draw  a  square  yard. 

A  square  whose  side  is  one  rod  is  a 
Square  Rod.  Measure  a  square  rod  in  your  schoolroom. 

A  square  whose  side  is  one  mile  is  a  Square   Mile. 
Section  of  land  is  a  square  mile. 

Draw  a  square  yard 
on  the  blackboard. 
Divide  each  side  into 
feet  and  connect  the 
division  marks  as  in 
the  figure.  How  many 
squares  are  there  ? 
What  is  each  square  ? 
How  many  square  feet 
are  there  in  one  square 
yard  ? 

NOTE. — Be  sure  to  make 
the  figure  on  the  black- 
board full  size. 

Divide  the  sides  of  one  of  these  square  feet  into  twelve 
equal  parts.  Connect  the  division  marks. 

How  many  squares  have  you  made  ?    What  is  each  square  ? 

How  many  square  inches  make  one  square  foot  ? 

In  a  similar  manner  you  might  divide  the  sides  of  a  square 
mile  into  320  rods  each,  making  320  x  320  =  102400  square 


198  PRIMARY   ARITHMETIC 

rods  in  one  square  mile.  Each  square  mile,  however,  is 
divided  into  640  acres.  This  makes  how  many  square  rods 
in  one  acre  ? 

You  might   also   divide  a  square  rod  into  5^  x  5J  =  30^ 
square  yards. 

228.    The  foregoing  demonstration  gives  us  the  following 


TABLE  OF  SURFACE  MEASURES 

144  square  inches  (sq.  in.)  make  1  square  foot  (sq.  ft.). 

9  square  feet  make  1  square  yard  (sq.  yd.). 
30|  square  yards  make  1  square  rod  (sq.  rd.). 
160  square  rods  make  1  acre  (A.). 
640  acres  make  1  square  mile  (sq.  mi.). 


229.    Written. 

1.  How  many  square  inches  in  3  sq.  feet?    in  6  sq.  ft.? 

2.  How  many  square  yards  in  54  sq.  feet  ?    in  108  sq.  ft.? 

3.  In  12|  sq.  ft.  how  many  sq.  inches? 

4.  How  many  acres  in  480  square  rods?    in  640  sq.  rd.? 

5.  In  7212  sq.  in.,  how  many  sq.  feet? 

6.  In  40  acres,  how  many  square  rods? 

7.  In  J  of  an  acre,  how  many  sq.  rods? 

8.  A  farmer  had  a  section  of  land.     He  sold  J  of  it  to 
one  man   and  ^  to  another.     How  many  acres  had  he  left  ? 
What  part  of  the  farm  is  left  ? 

9.  3  square  feet  is  what  part  of  a  square  yard  ? 

10.  What  part  of  a  square  foot  is  36  square  inches  ?     108 
•sq.  in.? 

11.  What  part  of  an  acre  is  120  square  rods  ? 


CUBIC   MEASURES 


199 


CUBIC   MEASURES 

230.    That  which  has  length  breadth,  and  thickness  is  a 
Solid. 


231.  A  solid  which  has  six  equal 
square  faces  is  a  Cube. 

A  cube  whose  edge  is 
one  inch  is  a  Cubic  Inch. 

A  cube  whose  edge  is 
one  foot  is  a  Cubic  Foot. 

A  cube  whose  edge  is 


Cube 


Cubic  inch 


one  yard  is  a  Cubic  Yard. 


3  Feet 


A  solid  3  feet  long,  1  foot  wide,  and  1  foot  high  contains 
how  many  cubic  feet?  (3  x  1  x  1.)  (See  picture.) 

A  solid  3  feet  long,  3  feet  wide,  and  1  foot  high  contains 
how  many  cubic  feet  ?  (3x3x1.)  (See  picture.) 

A  solid  3  feet  long,  3  feet  wide,  and  3  feet  high  contains 
how  many  cubic  feet  ?  (See  picture.) 

A  cubic  yard  is  how  many  feet  long,  wide,  and  high  ? 

Therefore,  a  cubic  yard  contains  how  many  cubic  feet  ? 

A  solid  12  inches  long,  1  inch  wide,  and  1  inch  high  con- 
tains how  many  cubic  inches  ? 


200  PRIMARY   ARITHMETIC 

A  solid  12  inches  long,  12  inches  wide,  and  1  inch  high 
contains  how  many  cubic  inches  ? 

A  solid  12  inches  long,  12  inches  wide,  and  12  inches  high 
contains  how  many  cubic  inches  ?  How  many  cubic  feet  ? 

Therefore,  a  cubic  foot  contains  how  many  cubic  inches  ? 

232.  The  answers  to  the  above  questions  give  us  the 
following 


TABLE    OF    CUBIC    MEASURES 

1728  cubic  inches  (cu.  in.)  make  1  cubic  foot  (cu.  ft.). 
27  cubic  feet  make  1  cubic  yard  (cu.  yd.). 


Written. 

1.  How  many  cu'bic  inches  in  6  cubic  feet  ?     in  8  cu.  ft.  ? 

2.  How  many  cubic  feet  in  8640  cubic  inches  ?     in  11,232 
cu.  in.  ? 

3.  How  many  cubic  inches  in  |  of  a  cubic  foot  ?  in  |  cu.  ft.  ? 

4.  What  part  of  a  cubic  foot  is  576  cubic  inches  ?    1152 
cu.  in.  ? 

5.  What  part  of  a  cubic  yard  is  3  cubic  feet  ?  9  culjic  feet? 

6.  What  will  it  cost  to  remove  an  embankment  containing 
54,000  cu.  ft.  of  earth  at  12|  cents  a  cubic  yard  ? 

LIQUID   MEASURES 


1  Gill  1  Pint  1  Quart  1  Gallon 


LIQUID   MEASURE  201 

233.  Fill  a  gill  cup  with  water.     Pour  it  into  a  pint  cup. 
Repeat  until  the  pint  cup  is  full.     How  many  times  have 
you  filled  the  gill  cup  ?     How  many  gills  in  one  pint  ?     Fill 
a  pint  cup  and  pour  into  a  quart  cup  until  the  quart  cup  is 
full.     How  many  pints  in  one  quart  ?     Fill  a  gallon  measure 
with  the  quart  cup.      How  many  quarts  in  one  gallon  ?     If 
you  should  fill  a  barrel  with  the  gallon  measure,  you  would 
need  to  fill  the  gallon  measure  31|-  times.     How  many  gal- 
lons make  one  barrel  ?     Two  barrels  of  water  would  fill  a 
hogshead.     How  many  gallons  in  a  hogshead  ? 

234.  From  this  work  we  may  make  the  following 


TABLE    OF    LIQUID    MEASURES 

4    gills  (gi.)  make  1  pint  (pt.). 
2    pints  make  1  quart  (qt.). 

4    quarts         make  1  gallon  (gal.). 
31 1  gallons        make  1  barrel  (bbl.). 
2    barrels        make  1  hogshead  (hhd.). 


These  denominations  are  sometimes  used  : 

2  hhd.  =  1  pipe  (pi.). 
2  pi.      =1  tun. 
Oral. 

1.  How  many  pint  cups  can  be  filled  from  8  quarts  ? 

2.  A  quart  of  milk   was  taken  from   a  five-gallon  pan. 
How  much  was  left  ? 

3.  How  many  gallons  in  a  hogshead  ? 

4.  f  of  a  gallon  are  how  many  quarts  ? 

5.  How  many  hogsheads  will  8  barrels  of  oil  fill  ? 


202  PRIMARY   ARITHMETIC 

DRY  MEASURES 


235,  Fill  a  pint  measure,  which  is  used  for  dry  measures, 
and  empty  it   into  a   quart  measure,   continuing   until  the 
latter    is    full.     How  many    times    must    you    fill    the   pint 
measure  ?      How  many  pints   in   1   quart  ?     Fill  the   quart 
(dry)  measure   and  empty   into  a  peck  measure   until  the 
latter  is  filled.     How  many  quarts  in  1  peck?     In  the  same 
way  find  how  many  pecks  in  1  bushel.      (Sawdust  or  oats 
may  be  conveniently  used  for  this  measurement.) 

236.  From  this  work  we  may  make  the  following : 


TABLE   OF    DRY   MEASURES 

2  pints  (pt.)  make  1  quart  (qt.). 
8  quarts  make  1  peck  (pk.). 

4  pecks  make  1  bushel  (bu.). 


Oral. 

1.  How  many  pecks  in  9  bushels  ? 

2.  In  22  pints,  how  many  quarts  ? 

3.  A  bushel  of  apples  at  $  .25  a  peck  will  cost  what  ? 

4.  How  many  pints  are  in  6  qt.  1  pt.  ? 

5.  What  will  a  peck  of  chestnuts  bring  if  sold  at  10  f  a 
quart  ? 

6.  How  many   times  can   a  quart    cup   be   filled  from   a 
bushel  of  walnuts? 

7.  How  many  quarts  are  in  9  pecks  ? 


AVOIRDUPOIS   WEIGHT 


203 


AVOIRDUPOIS  WEIGHT 


237.    Avoirdupois  weight  is  used  in  weighing  all  common 
articles,  as  coal,  groceries,  hay,  etc. 


TABLE    OF    AVOIRDUPOIS   WEIGHT 

16  drams  (dr.)  make  1  ounce  (oz.). 

16  ounces  make  1  pound  (lb.). 

25  pounds  make  1  quarter  (qr.). 

4  quarters  make  1  hundred-weight  (cwt.). 
20  hundred-weight  make  1  ton  (T.). 

2000  pounds  make  1  ton. 


The  avoirdupois  pound  contains  7000  grains. 
The  hundred-weight  is  sometimes  called  a  cental. 


204  PRIMARY   ARITHMETIC 

Oral.    , 

1.  How  many  ounces  are  in  4  pounds  ? 

2.  In  32  drams,  how  many  ounces  ? 

3.  What  will  a  pound  of  candy  cost  at  $.02  an  ounce  ? 

4.  How  many  pounds  in  4  tons  ? 

5.  In  6000  lb.,  how  many  tons  ? 

6.  How  many  pounds  are  in  a  hundred-weight  ? 

7.  Paid  $  .48  a  pound  for  candy.     How  much  is  that  an 
ounce  ? 

8.  How  many  3-pound  packages  can  be  made  from  75 
pounds  of  coffee  ? 

Written. 

1.  How  many  ounces  are  there  in  25  lb.  ? 

2.  In  7 1  tons,  how  many  pounds  ? 

3.  How  many  bullets  weighing  2  oz.  each  can  be  made 
from  32  lb.  4  oz.  of  lead  ? 

4.  What  will  2  J  lb.  dried  peaches  cost  at  $  .32  per  pound  ? 

5.  In  1364  drams,  how  many  ounces  ? 

6.  Five  boys  share  equally  1  lb.  9  oz.  of  candy.     How 
many  ounces  do  each  receive  ? 

7.  How  many  4-ounce  bags  can  I  fill  from  a  box  holding 
7  J  lb.  of  candy  ? 

8.  What  is  the  difference  in  ounces  between  a  hundred- 
weight and  97 \  pounds? 

9.  What  will  7|  lb.  of  indigo  cost  at  $.03  an  ounce  ? 

10.  Reduce  18^  lb.  to  ounces. 

11.  A  hundred-weight  is  what  part  of  a  ton  ? 


APOTHECARIES'   WEIGHT  205 

TROY  WEIGHT 

238.    Troy  weight  is  used  for  weighing  gold,  silver,  and 
precious  stones. 


TABLE    OF   TROY   WEIGHT 

24  grains  (gr.)     make  1  pennyweight  (pwt.). 
20  pennyweights  make  1  ounce  (oz.). 
12  ounces  make  1  pound  (lb.). 


Can  you  tell  why  Troy  weight  has  no  larger  denomination 
than  pounds  ? 

Oral. 

1.  How  many  ounces  in  2  lb.  ?     5  lb.  ?     10  lb.  ? 

2.  How  many  ounces  in  100  pwt.  ?     200  pwt.  ?     80  pwt.? 

3.  How  many  pwt.  in  96  grains  ?     72  gr.  ? 

4.  How  many  gr.  in  1  pwt.  ?     in  2  pwt.  ?     in  10  pwt.  ? 

5.  How  many  lb.  in  96  oz.?     in  120  oz.  ? 

6.  How  many  grains  in  half  an  ounce  of  gold  ? 

7.  A  watch  chain  weighs  10  pwt.     What  part  of  an  ounce 
does  it  weigh  ?     How  many  grains  ? 

APOTHECARIES'  WEIGHT 

239.  Apothecaries'  weight  is  used  by  physicians  and  drug- 
gists in  compounding  medicines,  and  by  druggists  in  selling 
medicines  in  quantities  smaller  than  one  ounce.  Medicines 
in  quantities  of  one  ounce  and  more  are  bought  and  sold  by 
Avoirdupois  weight. 


206  PRIMARY   ARITHMETIC 


TABLE  OF  APOTHECARIES'  WEIGHT 
20  grains  (gr.)  make  1  scruple  (sc.  or  3). 
3  scruples  make  1  dram  (dr.  or  3). 

8  drams  make  1  ounce  (oz.  or  5). 

12  ounces  make  1  pound  (Ib.  or  Ib). 


Oral. 

1.  How  many  grains  in  1  dram  ?     in  1  ounce  ? 

2.  How  many  drams  in  1  Ib.  ?     in  30  scruples  ? 

3.  How  many  pounds  in  144  ounces  ?     in  292  drams  ? 

4.  An  ounce  of   quinine   will   make   how  many   4-grain 
powders  ? 

5.  How  many  drams  will  make  sixty  3-grain  tablets  ? 

240.  FEDERAL  MONEY 


TABLE  OF  FEDERAL  MONEY 

10  mills  (m.)  make  1  cent  (ct.). 
10  cents  make  1  dime  (di.). 

10  dimes  make  1  dollar  ($). 

10  dollars         make  1  eagle  (E.). 


Oral. 

1.  How  many  dimes  in  6  dollars  ? 

2.  4  eagles  are  how  many  dollars  ? 

3.  A  man  had  $80  in  eagles.     How  many  eagles  had  he? 

4.  How  many  mills  in  15  cents  ? 

5.  In  5  dimes,  how  many  cents  ? 

6.  A  dollar,  a  quarter,  a   dime,   and   a   nickel   are  how 
many  cents  ? 

7.  How  many  dollars  are  there  in  130  dimes  ? 

8.  How  many  dollars  are  there  in  1300  cents? 


TIME 


207 


9.    Divide  4  eagles  among  5  men.     How  much  will  each 


receive : 

10.  How  many  books  at  50^  each  can  be  bought  for  $2  ? 

11.  How  many  dollars  in  a  double  eagle  ? 

TIME 

2*1.    The  solar  year  is  365^  days,  nearly. 

For  convenience  365  days  is  taken  for  a  common  year. 
The  \  day,  in  4  years,  amounts  to  another  day,  making 
every  4th  year  366  days.  This  is  called  leap  year.  This 
extra  day  is  added  to  February. 

Days  in  each  month: 
January  31  days.    July  31  days. 
February  28   or   August  31  days. 

29  days.  September  30  days. 

March  31  days.      October  31  days. 
April  30  days.        November  30  days. 
May  31  days.         December  31  days. 
June  30  days. 


TABLE   OF   TIME 


60  seconds  (sec.)  make  1  minute  (min.). 


60  minutes 
24  hours 

365  days 

366  days 

Also: 

7  days 


make  1  hour  (h.). 
make  1  day  (da.), 
make  1  common  year  (y.)- 
make  1  leap  year. 

make  1  week  (wk.). 


12  months  (mo.)  make  1  year. 
100  years  make  1  century. 


208  PRIMARY   ARITHMETIC 

Oral. 

1.  How  many  minutes  in  2  hours  ?     \  hour  ?     2£  hours  ? 

2.  Reduce  to  hours :    180  minutes,  120  minutes,  30  min- 
utes. 

3.  How  many  hours  in  a  week  ? 

4.  How  many  days  in  March  and  June  ? 

5.  What  4  months  have  30  days  ? 

6.  How  many  have  all  the  rest  except  February  ? 

7.  What  part  of  an  hour  is  45  minutes  ?     (Question.) 

Written. 

1.  If  a  boy  walk  \  mile  in  ten  minutes,  how  long  will  it 
take  him  to  walk  16  miles  ? 

2.  How  many  hours  in  the  month  of  August  ? 

The   winter   months    are    December,   January,   and    Feb- 
ruary. 

The  spring  months  are  March,  April,  and  May. 

The  summer  months  are  June,  July,  and  August. 

The  autumn  months  are  September,  October,  November. 

3.  Which  is  the  shortest  season  ?     Why  ? 

4.  Is  it  the  shortest  in  leap  year  ? 

5.  How  many  more  days  in  this  year  ? 


MISCELLANEOUS 

12  units  or  things,  1  dozen  (doz.). 

12  dozen,  1  gross  (gro.). 

20  units,  1  score. 
196  lb.,  1  barrel  of  flour. 
200  lb.,  1  bbl.  of  beef,  pork,  or  fish. 
280  lb.,  1  barrel  of  salt. 


REDUCTION   OF   DENOMINATE   NUMBERS  209 


TABLE   OF    PAPER   MEASURE 

24  sheets     make  1  quire. 
20  quires     make  1  ream. 

2  reams      make  1  bundle. 

5  bundles  make  1  bale. 


242.  Oral. 

1.  How  many  are  3  gross  of  pencils  ? 

2.  What  is  the  cost  of  \  gross  of  pens  at  60  ^  a  gross  ? 

3.  How  many  are  3  score  years  ? 

4.  How  many  are  3  score  and  10  years  ? 

5.  How  many  are  5  dozen  eggs  ?  6|  dozen  eggs  ? 

6.  How  many  sheets  in  3  quires  of  paper  ? 

7.  How  many  quires  in  ^  a  ream  ? 

8.  84  eggs  are  how  many  dozen  ? 

9.  How  many  reams  in  a  bale  of  paper  ? 

10.  How  many  pounds  in  ^  bbl.  of  flour  ? 

Written. 

11.  How  many  dozen  in  66  cucumbers  ? 

12.  What  is 'the  cost  of  6  quires  of  paper  at  $4  a  ream  ? 

13.  What  will  8  gross  of  copy-books  cost  at  10^  apiece  ? 

14.  If  paper  is  bought  at  $2  a  ream  and  sold  at  18^  a 
quire,  what  is  the  gain  on  6  reams  ? 

REDUCTION   OF   DENOMINATE   NUMBERS 

243.  Changing  numbers  to  smaller  denominations  is  Re- 
duction Descending. 

Changing  numbers  to  larger  denominations  is  Reduction 
Ascending. 

What  is  reduction  (see  definition,  Art.  129)  ?  In  reduction 
of  numbers,  what  is  changed  ?  What  is  not  changed  ? 


210 


PRIMARY  ARITHMETIC 


l.    Reduce  2  Ib.  7  oz.  5  pwt.  17  gr.  to  grains. 


2. 


2  (Ib.) 
12  oz. 
24  oz. 
+  7  oz. 
~31  (oz.) 
_20  pwt. 
620  pwt. 
+  5  pwt. 
625  (pwt.) 
24  gr. 
2500 
1250 

15000  gr. 

+  17  gr. 

15017  gr. 


How  many  oz.  are  there  in  1  Ib.  ? 
How  many  oz.  are  there  in  2  Ib.  ? 
24  oz.  +  7  oz.  =  how  many  oz.  ? 
How  many  pwt.  are  there  in  1  oz.  ? 
How  many  pwt.  are  there  in  31  oz.  ? 
620  pwt.  -f  5  pwt.  =  how  many  pwt.  ? 
How  many  gr.  are  there  in  1  pwt.  ? 
How  many  gr.  are  there  in  625  pwt.  ? 
15000  gr.  +  17  gr.  =  how  many  gr.  ? 


Ans. 


Reduce  2  mi.  51  rd.  2  yd.  2  ft.  7  in.  to  inches. 

2  (mi.) 

320  rd. 

640  rd. 

-f  51  rd. 

2~|691  (rd.) 


How  many  rods  are  there  in  1  mi.     In  2  mi.? 

640  rd.  +  51  rd.  =  how  many  rods  ? 

How  many  yd.  in  1  rod  ?     In  691  rd.  ? 

38001  yd.  +  2  yd.  =  how  many  yd.  ? 

How  many  feet  in  1  yard?     In  3802J  yards? 

11407J  ft.  +  2  ft.  =  how  many  feet  ? 

In  1  foot  there  are  how  many  inches?     IP  114091 

feet? 
136914  in.  -f  7  in.  =  how  many  inches? 


345| 
3455 
3800J  yd. 

-f  2    yd. 
38021  (yd.) 
3 


11407|  ft. 
+  2  ft. 
11409J  (ft.) 
12 


6  in. 

136908  in. 
136914  in. 
+  7  in. 
136921  in.  .4ns. 


REDUCTION   DESCENDING  211 

244.    From  the  above  examples  we  may  make  the  following 


Rule  for  Reduction  Descending 

Multiply  the  number  of  the  largest  denomination  given 
by  the  number  of  units  of  the  next  smaller  denomina- 
tion which  are  equal  to  one  unit  of  the  denomination 
multiplied.  To  this  product,  add  the  given  number  of 
the  same  denomination  as  the  product.  Proceed  in  the 
same  way  with  this  and  each  succeeding  result  until 
the  required  denomination  is  reached. 


3.    Reduce  2  sq.  mi.  125  A.  71.  sq.  rd.  1  sq.  yd.  to  square 

yards. 

2  (sq.  mi.) 
640  A. 
1280  A. 
+  125  A. 
1405  (A.) 

160  sq.  rd. 
84300 
1405 

224800  sq.  rd. 
+  71  sq.  rd. 
224871  (sq.  rd.) 

121  fourths  sq.  yd.     NOTE. — 30£  sq.  yd.  = 
224871  ifi  sq.  rd. 

449742 
224871 

4  fourths  |  27209391  fourths  sq.  yd. 
68023471  sq.  yd.     Ans. 
245. 

Reduce  to  lower  denominations  : 

4.  17  yd.  2  ft.  9  in.  to  inches. 

5.  46  rd.  4  yd.  2  ft.  to  feet. 


212  PRIMARY    ARITHMETIC 

I 

6.  3  mi.  75  rd.  4  ft.  to  inches. 

7.  16  A.  140  sq.  rd.  26  sq.  yd.  to  square  yards. 

8.  4  A.  15  sq.  rd.  4  sq.  ft.  to  square  inches. 

9.  16  cu.  yd.  25  cu.  ft.  900  cu.  in.  to  cubic  inches. 

10.  15  gal.  3  qt.  1  pt.  to  pints. 

11.  7  bu.  3  pk.  5  qt.  1  pt.  to  pints. 

12.  16^  bu.  to  quarts. 

13.  25  Ib.  5  oz.  16  pwt.  10  gr.  to  grains. 

14.  2  T.  6  cwt.  10  Ib.  14  oz.  to  ounces. 

15.  What  will  3  reams  of  paper  cost  at  40  ^  a  quire  ? 

16.  Reduce  3  mi.  4  fur.  20  rd.  5  yd.  2  ft.  8  in.  to  inches. 

17.  Reduce  6  mi.  240  rd.  to  feet. 

18.  Reduce  3  A.   8  sq.  rd.  5  sq.  yd.  3  sq.  ft.  to  square 
inches. 

19.  Reduce  16  cu.  yd.  9  cu.  ft.  3  cu.  in.  to  cubic  inches. 

20.  Reduce  2  T.  3  ctl.  16  Ib.  to  ounces. 

21.  Reduce  3  Ib.  9  oz.  15  pwt.  12  gr.  to  grains. 

22.  Reduce  60  gal.  3  qt.  3  gi.  to  gills. 

23.  How  many  sheets  in  5  bales  of  paper  ? 

24.  Reduce  3  wk.  6  da.  5  hr.  to  minutes. 


REDUCTION  ASCENDING 
246.    1.    Reduce  5499  qt.  to  bushels. 


8  qt. 
4pk. 


How  many  qt.  in  1  pk.  ? 

5499  qt.  5499  qt.  =  how  many  pk.  ? 

687  pk.  -f  3  qt.          How  many  qt.  over  ? 
171  bu.  +  3  pk.         How  many  pk.  in  1  bu.? 
J  pk.  3  qt.    Ans.         687  pk.  —  how  many  bu.? 
How  many  pk.  over  ? 


A.I  A     IL»IA.     "| 

How  many  pk.  over 


REDUCTION   ASCENDING 


213 


2.    Reduce  241329  in.  to  larger  denominations. 


12  in. 

3ft. 

11  half 

yd- 

241329  in. 

20110  ft.  +  9  in. 

6703  yd.  +  1  ft. 
2 

13406  half  yd. 

1218  rd.  +  8  half  yd. 

=  4  yd. 

3  mi.  +  258  rd. 


320  rd.)121£  rd. 
96^ 
258  rd. 

3  mi.  258  rd.  4  yd.  1  ft.  9  in.   Ans. 


How  many  inches  make  1 
ft? 

How  many  feet  in  241329 
in.? 

How  many  inches  left  ? 

How  many  ft.  make  1  yd.  ? 

How  many  yd.  in  6703  ft.  ? 

How  many  feet  left? 

How  many  yd.  in  1  rd.  ? 
How  many  half  yd.  ? 

How  many  half  yd.  in  6703 
yd.? 

How  many  rd.  in  13406  half 
yd.? 

How  many  half  yd.  over? 
8  half  yd.  =  how  many  yd.  ? 

How  many  rd.  in  1  mi.? 

How  many  mi.  in  1218  rd.  ? 

How  many  rd.  left  ? 


3. 


Reduce  208824  sq.  in.  to  larger  denominations. 


1450  sq.  ft. 
144)208824 
144 
648 
576 
722 
720 

24  sq.  in. 


f  sq.  yd.  =  6  sq.  ft.  108  sq.  in. 
5  sq.  rd.  9|  sq.  yd.  1  sq.  ft.  24  sq.  in.  — 
5  sq.  rd.  9  sq.  yd.  7  sq.  ft.  132  sq.  in.  Ans, 


9  [1450  sq.  ft. 

161  sq.  yd.  -f  1  sq.  ft. 

4 
121  fourths)_644  fourths  sq.  yd. 


5sq.  yd.  +  \9  sq.  yd.  =  9|  sq.  yd. 


214  PRIMARY  ARITHMETIC 


Rule  for  Reduction  Ascending 

Divide  the  given  number  by  the  number  of  units  of 
the  denomination  given  which  are  equal  to  one  unit  of 
the  denomination  next  larger.  Keep  the  remainder, 
if  any,  as  part  of  the  answer. 

Proceed  in  the  same  manner  with  this  and  each  suc- 
ceeding quotient  till  the  required  denomination  has 
been  reached. 


247.   4.    Reduce  225932  inches  to  miles,  etc. 

5.  How  many  miles  and  rods  are  there  in  35640  ft.  ? 

6.  Reduce  19922544  sq.  in.  to  larger  denominations. 

7.  Reduce  762051  cu.  in.  to  cubic  yards,  etc. 

8.  Reduce  69056  oz.  to  tons,  etc. 

9.  Reduce  21076  gr.  to  larger  denominations. 

10.  Reduce  1947  gi.  to  gallons,  etc. 

11.  How  many  bales  in  24000  sheets  of  paper  ? 

12.  Reduce  39180  min.  to  weeks,  etc. 

13.  How  many  bushels,  etc.,  in  35842  pints  ? 

14.  How  many  pounds,  etc.  (Troy),  in  32563  gr.  ? 

15.  Reduce  39632  gr.  to  pounds,  etc.  (apoth.). 

16.  How  many  tons,  etc.,  in  35682  Ib.  ? 

17.  A  box  contains  75832  pens.     How  many  great  gross, 
etc.,  in  the  box  ? 

18.  Change  1384  dry  pints  to  larger  denominations. 

19.  In  139843  sq.  in.  how  many  square  rods,  etc.  ? 

20.  Reduce  164808  in.  to  miles,  etc. 

21.  In  12024  in.  how  many  rods,  etc.  ? 


REVIEW   OF   REDUCTION  215 

248.  Written  Review. 

1.  How  many  2-quart  cups  can  be  filled  from  a  barrel  of 
syrup  ? 

2.  Change  7  gal.  2  qt.  1  pt.  to  gills. 

3.  In  276  pints  how  many  gallons  ? 

4.  A  merchant  paid  $10  for  a  barrel  of  molasses,  and 
retailed  it  at  $  .40  a  gallon.     What  was  his  gain  ? 

5.  How  many  ounces  are  there  in  250  Ib.  ? 

6.  In  17|  tons  how  many  pounds  ? 

7.  How  many  bullets  weighing  |  oz.  each  can  be  made 
from  32  Ib.  4  oz.  of  lead  ? 

8.  Reduce  118  Ib.  7  oz.  to  drams. 

9.  Reduce  15  pk.  7  qt.  to  pints. 

10.  How  many  quarts  are  in  846  pints  ? 

11.  Henry  gathered  16  bu.    2  qt.  of  walnuts,  and  sold 
them  at  $  .08  a  quart.     What  did  he  receive  for  them  ? 

12.  In  8136  pt.  how  many  bushels,  etc.  ? 

13.  What  will  6  bu.  2  pk.  of  cranberries   be  worth  at 
1.75  a  peck? 

14.  A    half-barrel    of   vinegar  was   sold  at   2^  a  quart. 
What  was  received  for  it  ? 

15.  How  many  gallons  in  16  quarts  ? 

16.  13|  gallons  have  been  sold  from  a  barrel.     How  many 
quarts  are  left  ? 

17.  At  7  ^  a  quart  what  will  15  gal.  of  vinegar  cost  ? 

18.  How  many  quarts  are  there  in  7  bu.  3  pk.  7  qt.  ? 

19.  A  peck  of  peaches  was  sold  .from  a  crate  containing 
a  bushel.     How  many  quarts  were  left  ? 

20.  How  many  bushels  are  there  in  576  pints  ? 


216  PRIMARY   ARITHMETIC 


ADDITION   OF   COMPOUND   NUMBERS 

249.     l.    Add  14  Ib.  5  oz.   17  pwt.   12  gr.,  18  Ib.  10  oz. 
14  gr.,  6  Ib.  4  oz.  8  pwt.  16  gr. 

Ib.    -    oz.    pwt.    gr. 

14        5     17      12  SOLUTION.  — The  sum  of  the   grains  =  42   gr. 

=  1  pwt.  18  gr.     We  place  the  18  gr.  under  the 

column  of  grains,  and  add  the  1  pwt.  to  the  column 

6        4        8      16      of  pennyweights.     Add  the  other  columns  in  like 

39       8      6     18     manner- 

rd.        yd.      ft. 
2.          17        4        1  3. 

12      4       2 

6       5       21 

832 
46       1|     li 


46       2       0 


bu. 

Pk. 

qt. 

4. 

Add:     7 

1 

3 

10 

1 

2 

4 

1 

2 

yd. 

ft. 

in. 

6. 

1 

2 

6 

2 

1 

1 

2 

3 

5. 


7. 


Find  the  sum : 

8.  3  bu.  2  pk.  2  qt.  1  pt. ;  4  bu.  5  pk.  3  qt.;   7-  bu.  1  pk. 
4  qt.   1  pt. 

9.  7  Ib.  8  oz.  6  dr. ;  4  Ib.  11  oz.  5  dr. ;    2  Ib..  4  dr. 

10.    1  bbl.   14  gal.   2  qt.   1  pt. ;.    2  bbl.   5  gal.   3  qt. ;   7  gal. 
3  qt. 


rd. 

ft. 

in. 

6 

12 

6 

4 

14 

11 

17 

15 

9 

6 

12 

8 

36 

5| 

10 

6  =  £  ft. 

36 

6 

4 

bbl. 

6 

gal. 

7 

qt. 
1 

5 

12 

1 

4 

6 

1 

bbl. 
4 

gal 

7 

qt.     pt. 
4     1 

6 

2 

1 

3 

5 

1     1 

SUBTRACTION  OF  COMPOUND  NUMBERS  217 

SUBTRACTION  OF   COMPOUND  NUMBERS 

Ib.     oz.    pwt.     gr.  SOLUTION.  — 15  gr.  -  12  gr. 

250.    1.    From   6        2      14      15       =  3  gr.     As   we   cannot  take 

Take    4      10      18      12      18  pwt.  from  14  pwt.,  we  take 

1        3      16        3      ^  oz>'  wh*ch  equals  20  pwt.,  and 

add  to  the  14  pwt.  =  34  pwt.; 

34  pwt.  —  18  pwt.  —  16  pwt.  We  have  taken  1  oz.  from  the  2  oz.,  leaving 
1  oz.;  but  as  we  cannot  take  10  oz.  from  1  oz.,  we  take  1  Ib.  =  12  oz.,  and 
add  it  to  1  oz.  =  13  oz.,  from  which  take  10  oz.  =  3  oz.  Since  we  took  1 
of  the  6  Ib.,  we  have  5  Ib.  left;  from  which  take  4  Ib.  =  1  Ib. 


A. 

sq.  rd. 

sq.  ft. 

hr. 

min. 

sec. 

2. 

From 

10 

50 

7 

4.   5 

54 

30 

Take 

4 

106 

5 

1 

71 

50 

da. 

hr. 

min. 

sec. 

T. 

cwt. 

Ib. 

OZ. 

3. 

200 

17 

54 

36 

5.  20 

15 

75 

10 

135 

20 

24 

48 

5 

16 

25 

12 

Subtract  : 

6.  16  Ib.  8  oz.  3  dr.  8.      7  yd.  3  ft.  9  in. 

542  257 

7.  16  da.  5  hr.  36  min.  9.    27  gal.  3  qt.  1  pt.  2  gi. 

5        7         18  18         2  S 


10.  From  6  dol.  7  di.  2  ct.  3  m.  take  4  dol.  5  di.  8  ct.  1  m. 

11.  Find  the  difference  between  4  Ib.  8  oz.  3  dr.  and  2  Ib. 
5  oz.  7  dr. 

12.  From  a  can  containing  7  gal.  2  qt.  1  pt.  of  milk,  4  gal. 
3  qt.  were  sold.     How  much  was  left  ? 

13.  6  ft.  11  in.  were  cut  from  a  pole  18  ft.  9  in.  long.    How 
long  was  the  pole  then  ? 


218  PRIMARY   ARITHMETIC 

251.   1.    Find  the  time  from  Jan.  25,  1842,  to  July  4,  1896. 
It  is  customary  to  consider  30  days 

yr.  mo.          da. 

1896         7  4  to   a   month.      July   4,    1896,   is   the 

1842         1         25  1896th  year,  7th  month,  4th   day  of 

54 5 g  the  Christian  Era,  and  Jan.  25,  1842, 

is    the    1842d   year,    1st    month,    and 

25th  day.     Subtract,  taking  30  days  for  a  month. 

2.  What  is  the  exact  number  of  days  between  Dec.  16, 
1895,  and  March  12,  1896  ? 

Dec.      15  Do  not  count  the  first  day  mentioned. 

Jan.       31  There  are  15  days  in  December  after  the 

Feb.      29  16th.     January  has  31  days,  February 

March  12  29  (leap  year),  and  March  12,  making 

87  days  Ans.    87  days.     Always  count  the  last  day. 

3.  Find  the  time  between  Dec.  11,  1620,  and  July  4,  1776. 

4.  How  much  time   elapsed   from   the   beginning   of   the 
Civil  War,  April  14,  1861,  to  the  close  of  the  war,  April  9, 
1865? 

5.  Washington  was  born  Feb.  22,  L732,  and  died  Dec.  14, 
1799.     How  long  did  he  live  ? 

6.  How  much   time  since  Oct.   12,  1492,  to  the  present 
time? 

7.  Mr.  Griffith  gave  a  note  dated  Feb.  25,  1896,  and  paid 
it  July  12,  1896.     Find  the  exact  number  of  days  between 
the  giving  and  the  paying  of  the  note. 

8.  Find  the  exact  number  of  days  between  June  25,  1900, 
and  Aug.  24,  1900. 

Find  the  exact  time  between 

9.    Sept.  6,  1896,  and  April  7,  1897. 

10.  Nov.  11,  1898,  and  Dec.  4,  1898. 

11.  Aug.  16,  1900,  and  Dec.  21,  1900. 


MULTIPLICATION  OF   COMPOUND  NUMBERS         219 

12.  July  4,  1896,  and  Aug.  10,  1896. 

13.  Feb.  23,  1897,  and  June  4,  1897. 

14.  Oct.  9,  1899,  arid  Feb.  6,  1900. 
is.  Nov.  8,  1894,  and  Oct.  6,  1895. 

MULTIPLICATION  OF  COMPOUND  NUMBERS 

252.    l.  Multiply  4  yd.  2  ft.  8  in.  by  8. 

SOLUTION. — 8  times  Sin.  =  64  in.  =  5  ft.  4  in.     Place 

'       '      the  4  in.  under  the  inches  column,  and  reserve  the  5  ft. 

to  be  added  to  the  product  of  2  ft.  by  8,  which  equals 

°        (adding  5  ft.)  21  ft.     21  ft.  —  7  yd.  with  no  remainder. 

39      0      4        Place  0  under  the  feet  column  and  add  7  yd.  to  the 
product  of  4  yd.  by  8,  which  -equals  (adding  the  7  yd.) 
39  yd.     The  product,  therefore,  is  39  yd.  4  in. 

2.  10  gal.  2  qt.  1  pt.  3  gi. 

6        • 

3.  12  bu.  2  pk.  5  qt.  1  pt. 


4.  How  much  hay  in  6  loads  if  each  load  weighs  1  T. 

2  cwt.  25  lb.? 

5.  What  is  the  weight  of  9  silver  spoons  if  each  weighs 

3  oz.  14  pwt.  14  gr.? 

6.  How  much   oil    in   5   barrels    if    each   barrel   contains 
35  gal.  2  qt.  1  pt.? 

7.  What   is   the  weight  of    8   packages   if   each  weighs 
1  lb.  4  oz.  (avoir.)  ? 

8.  A  farmer  has  6  bins,  each  containing  58  bu.  3  pk.  2  qt. 
How  much  wheat  in  the  bins  ? 

9.  A  farmer  can   plough   one  acre   of   ground   in   7  hr. 
20  min.  6  sec.     At  the  same  rate  how  long  will  it  take  him 
to  plough  8  acres  ? 


220  PRIMARY   ARITHMETIC 

DIVISION  OF  COMPOUND  NUMBERS 
253.    1.  Divide  16  Ib.  9  oz.  17  pwt.  7  gr.  by  5. 

lb.     oz.   pwt.    gr.         SOLUTION.. —  J  of  16  Ib.  =  3  Ib.  and  1  Ib.  re- 
5)16      9      17        7     maining.     1  lb.  =  12  oz.,  which  added  to  9  oz. 
g      4        *j      JY     —  21  oz.     \  of  21  oz.  =  4  oz.  with  1  oz.  remain- 
ing.    1  oz.  =  20  pwt.,  which  added  to  17  pwt. 

=  37  pwt.     I  of  37  pwt.  =  7  pwt.  and  2  pwt.  remaining.     2  pwt.  =  48  gr,. 
which  added  to  7  gr.  =  55  gr.     -|  of  55  gr.  =  11  gr. 
The  quotient,  therefore,  is  3  lb.  4  oz.  7  pwt.  11  gr. 

2.  Divide  54  bu.  3  pk.  3  qt.  by  5. 

3.  8  persons  share  equally  in  the  contents  of  a  bin  con- 
taining 20  bu.  2  pk.  of  apples.     What  is  the  share  of  each  ? 

4.  When  $6  will  buy  5  gal.  3  qt.  1  pt.  of  maple  syrup, 
how  much  will  $  1  buy  ? 

5.  If  a  horse  eats  8  qt.  of  oats  per  day,  how  long  will 
10  bu.  1  pk.  5  qt.  last  him  ? 

NOTE.  —  When  both  dividend  and  divisor  are  compound,  reduce  them 
to  the  same  denomination  and  divide.     The  quotient  will  be  abstract. 

6.  If  a  package  weighs  4  cwt.  15  lb.,  how  many  such 
packages  will  it  take  to  weigh  3  T.  2  cwt.  25  lb.  ? 

7.  Divide  102  T.  15  cwt.  27  lb.  8  oz.  by  8. 

8.  I  have  83  lb.  2  oz.  of  salt  which  I  wish  to  put  into 
packages    of  2  lb.   6  oz.  each.     How   many   packages   will 
there  be  ? 

9.  113  gal.  2  qt.  0  gi.  -*-  4  =  ? 

10.  126  gal.  3  qt.  1  pt.  -*-  6  =  ? 

11.  220  gal.  2  qt.  -*-  7  =  ? 

12.  6  T.  1200  lb.  -*•  5  =  ? 

13.  Divide  746  oz.  4  pwt.  by  7. 

14.  Divide  10  wk.  4  da.  3  hr.  8  min.  by  4. 


SURFACE   MEASU: 


221 


6  IN. 


SURFACE   MEASUREMENTS 

254.  A  plane  figure  having  four  straight  sides  and  four 
right  angles  is  a  rectangle. 

The  Area  of  a  surface  is  the  number  of  square  units  that 
it  contains. 

What  is  the  square  unit 
in  this  rectangle? 

How  many  square  inches 
in  it? 

There  are  how  many 
square  inches  in  a  row? 
There  are  how  many  rows  ? 

Therefore  how  many 
square  inches  ?  How  do 
you  find  it? 

The  length  and  breadth  of  a  rectangle  are  called  its 
Dimensions. 

NOTE. —  In  finding  areas,  as  in  all  multiplication,  the  multiplier  is 
abstract,  and  the  unit  of  the  product  must  be  the  same  as  the  unit  of 
the  multiplicand. 

255.  The  answers  to  these  questions  give  us  the  following: 


Rule  for  Finding  the  Area  of  a  Rectangle 

Multiply  the  length  by  the  breadth  expressed  in  the 
same  denomination.  The  result  will  be  the  area  ex- 
pressed in  square  units  of  the  denomination  correspond- 
ing to  that  of  the  dimensions. 


Oral. 

1.  How  many  square  feet  in  a  surface  6  ft.  long  and  1  ft. 
wide  ? 

2.  In  a  surface  6  ft.  long  and  2  ft.  wide  ? 


222  PRIMARY   ARITHMETIC 

3.  How  many  square  feet  in  a  platform  5  ft.  long  and 
4  ft.  wide  ? 

4.  What  is  the  area  of  a  mirror  3  ft.  long  and  2  ft.  wide  ? 

5.  Draw  a  rectangle  4  inches  long  by  2  inches  wide,  and 
divide  it  into  square  inches. 

6.  Draw  a  2-inch  square  and  divide  it  into  square  inches. 

7.  What  is  the  difference  between  a  2-inch  square  and  2 
square  inches  ? 

8.  How  many  square  feet  does  a  5-foot  square  contain  ? 
Show  the  difference  between  a  5-ft.  square  and  5  square  feet. 

9.  If  the  top  of  a  table  is  5  ft.  long  and  4  ft.  wide,  what 
is  its  area? 

10.    If   the   area  of   a  floor  is  20  square  yards,  and  the 
length  5  yards,  what  is  the  width  ? 


Principles 

1.  Area   is   the    product    of    length   multiplied    by 
breadth.    The  numbers  representing  length  and  breadth 
must  be  like  numbers. 

2.  Area  divided  by  either  dimension  gives  the  other. 


256.  Written. 

1.  How  many  square  feet  in  the  top  of  a  table  5  J  ft.  long 
and  4  feet  wide  ?     How  many  square  inches? 

2.  What  is  the  area  of  a  basement  36  ft.  by  18|-  ft.? 

3.  At  22^  a  square  foot,  what  is  the  cost  of  a  flag  walk 
50  ft.  x6  ft.? 

4.  How  wide  is  a  floor  whose  area  is  300  sq.  ft.  and  whose 
length  is  20  ft.? 

5.  5  flag-stones,  each  5|  ft.  by  6  ft.,  will  cover  how  much 
surface  ? 


PLASTERING   AND    PAINTING 


223 


6.  In  a  room  are  4  doors,  each  7  ft.  6  in.  by  2  ft.  8.  in. 
How  many  square  feet  in  the  surface  of   the    four  doors? 
How  many  square  inches  ? 

7.  A  pasture  containing  4  acres  is  20  rods  wide.     How 
long  is  it  ? 

8.  A  city  lot  containing  8400  sq.  ft.    is  140  ft.   deep. 
What  is  the  frontage  ? 

9.  How  many  acres  in  a  field  ^  mile  square  ? 

10.  Is  there  any  difference  between  a  mile  square  and  a 
square  mile  ? 

PLASTERING    AND    PAINTING 

257.  Plastering  and  painting  are  usually  done  by  the 
square  yard. 

Deductions  are  frequently  made  for  openings. 
Windows  and  doors  are  openings. 

l.  A  room  is  18  ft.  long,  12  ft.  wide,  and  10  ft.  high. 
How  many  square  yards  in  the  walls  and  ceiling  ? 

In  problems  of  this  kind  first  make  a  diagram  represent- 
ing the  four  walls  in  a  line. 

The  ceiling  may  be  represented  as  extend-        r-_i2  FT. 


ing  from  a  side  wall  or  an  end  wall. 

Draw  this  diagram  (enlarged)  on  stiff  paper, 
then  cut  and  fold  the  pattern  to  represent  the      * 
walls  and  ceiling  of  the  room. 


I 


12  FT. 


12  FT. 


SOLUTION.  —  The  length  of  the  four  walls  is  2  x  (18  ft.  +  12  ft.)  = 
60  feet. 


224  PRIMARY   ARITHMETIC 

Area  of  four  walls,  60  ft.  by  10  ft.  =  600  sq.  ft. 

Area  of  ceiling,  18  ft.  by  12  ft.  =  216  sq.  ft. 

Area  of  four  walls  and  ceiling  =  816  sq.  ft.  =  90  f  sq.  yd. 

2.  If  in  the  room  mentioned  above  there  are  two  doors, 
3  ft.  by  7  ft.,  and  four  windows  3  ft.  by  6  ft.,  how  many 
square  yards  remain  in  the  four  walls  and  ceiling  ? 

Represent  these  doors  and  windows  on  the  diagram. 

3.  How  much  will  it  cost  at  25  cents  a  square  yard  to 
plaster  the  room  mentioned  in  example  1,  full   deductions 
being  made  for  openings  ? 

4.  What  will  it  cost  at  33J  cents  a  square  yard  to  plaster 
the  walls  and  ceiling  of  a  room  24  ft.  long,  18  ft.  wide,  and 
9    ft.    high  ?     The  room  has  3  doors  3  ft.  by  7  ft.,  and  6 
windows  3  ft.  by  6  ft.     One-half  of  the  openings  deducted. 

5.  How  many  square  yards  of  plastering  in  a  room  40  ft. 
long,  30  ft.  wide,  and  12  ft.  high,  deducting  80  sq.  ft.  for 
openings  ? 

6.  At  35  ^  a  sq.  yard,  what  will  it  cost  to  plaster  a  room 
18  ft.  square  and  9  ft.  high,  having  3  doors  7  ft.  by  3  ft., 
and  5  windows  6  ft.  by  3  ft.,  no  allowance  for  openings  ? 

CARPETING   ROOMS 

258.  In  making  a  carpet,  the  carpeting  is  cut  from  a  roll 
into  strips  which  are  usually  laid  from  end  to  end  on  the 
floor,  or  lengthwise.  Sometimes  the  strips  are  laid  across 
the  room. 

l.  How  much  carpeting  1  yd.  wide  must  I  purchase  to 
cover  a  room  6  yd.  long  and  4|  yd.  wide,  strips  running 
lengthwise  ? 

SOLUTION.  —  It  will  be  necessary  to  purchase  as  much  carpeting  as  if 
the  room  were  5  yd.  wide,  the  excess  of  J  yd.  being  turned  under  in  the 
last  strip. 

1  strip  contains  6  yd.     5  strips  =  5  times  6  yd.  =  30  yd.     A  ns. 


CARPETING  225 

2.  How  many  yards  must  I 
purchase,  if  the  strips  are  laid 
across  the  room  ? 

SOLUTION.  —  1  strip  contains  4f 
yd.  6  strips  =  6  times  4f  yd.  =  28| 
yd.  Ans. 

Carpeting  is  commonly  1  yd. 
or  |  yd.  wide. 

NOTE.  —  It  is  often  necessary  to 
purchase  more  than  enough  carpeting 
to  cover  a  room,  on  account  of  the  waste  in  matching  patterns. 

This  diagram  represents  the  floor  in  example  1,  in  which 
the  strips  are  laid  lengthwise.  Pupils  should  draw  a  simi- 
lar diagram  for  each  floor. 

3.  How  many  yards  of  carpet  |  yd.  wide  will  be  required 
for  a  hall  18  ft.  wide  and  30  ft.  long,  the  strips  running  the 
long  way  of  the  hall  ? 

Make  a  diagram  showing  the  strips  or  breadths. 
How  many  linear  yards  in  each  strip  ? 
How  many  strips? 

SOLUTION.  —  Since  one  strip  covers  a  space  f  yd.  wide,  it  will  take  as 
many  strips  to  cover  a  space  6  yd.  wide,  as  {  yd.  is  contained  times  in  6 
yd.  —  8  strips. 

8  strips  each  10  yd.  long  =  80  linear  yards. 

How  many  yards  must  be  purchased  if  the  strips  run  the 
short  way  ? 

4.  At  11.25  a  yard,  what  will  it  cost  to  carpet  a  hall  11^ 
ft.  wide  and  28  ft.  long,  the  carpet  being  1  yard  wide  ? 

How  many  yards  long  is  each  strip? 
How  many  strips? 

5.  How  much  would  the  carpet  cost  if  there  were  a  waste 
of  1^  yd.  for  matching  ?     (Ex.  4.) 


226 


PRIMARY   ARITHMETIC 


7. 


6.  How  many  yards  of  ingrain  carpet  1  yd.  wide  will  be 
required  for  a  floor  17  ft.  wide  and  20  ft.  long,  strips  run- 
ning lengthwise? 

How  many  yards  long  is  each  strip  ? 

How  many  strips  would  be  needed  if  the  room  wera  15  ft. 
wide  ?  How  many  if  it  were  18  ft.  wide  ? 

It  being  17  ft.  wide,  how  many  strips  must  be  purchased  ? 

How  much  of  the  last  strip  is  to  be  turned  under  ? 

A  sidewalk  10  ft.  wide  is  to  be  laid  on  the  4  sides  of 

110  FT. t      a  lot    100  ft.  square.     At 

25^  a  sq.    foot,  what  will 
be  the  cost  ? 

The  walk  will  be  110 
ft.  long  on  each  of  the 
four  sides,  as  shown  by 
the  diagram.  The  entire 
length  of  the  walk  is  4  x 
110  ft.  =  440  ft. ;  this 
multiplied  by  the  width 
of  the  walk  will  give  its 
area. 


100  FT. 


100  FT. 


110  FT. 

8.  What  will  be  the  cost  of  a  5-foot  walk  laid  on  the 
inside  of  the  lot,  close  to  the  sides  ? 

9.  A  man  builds  a  house  45  by  35  ft.  on  a  lot  60  by  150 
ft.     How  many  sq.  yards  has  he  left  for  a  lawn  ? 

10.  What  will  it  cost  to  build  a  tight  fence  5  ft.  high 
around  the  above  lot  at  25  ^  a  square  yard  ? 

11.  What  is  the  cost  of  a  farm  80  rods  square  at  $  50  an 
acre  ? 

12.  How  long  is  a  rectangular  field  that  contains  50  acres 
and  is  80  rods  wide  ? 


PAPERING  WALLS  227 

PAPERING   WALLS 

259.  A  roll  of  paper  is  commonly  8  yards  long  and  18 
inches  wide. 

A  double  roll  is  16  yards  long. 
Borders  are  sold  by  the  linear  yard. 

1.  A  room  is  18  ft.  by  15  ft.,  and  9  ft.  high.     Making  no 
deduction  for  openings,  how  many  square  yards  in  the  four 
walls  and  ceilings  ? 

How  many  square  yards  will  one  roll  cover  ? 

How  many  rolls  will  be  needed  to  paper  the  room  ? 

If  the  room  has  2  doors  3  ft.  by  8|  ft.,  and  4  windows 
5  ft.  by  6|  ft.,  how' many  sq.  yards  "of  surface  are  to  be 
covered  ? 

How  many  rolls  will  cover  it  ? 

At  33  J  ^  a  roll,  what  will  be  the  cost  of  papering  ? 

At  50  ^  a  lineal  yard,  what  will  the  border  cost  ? 

2.  A  hall  is  12  ft.  wide,  38  ft.  long,  and  10  feet  high. 
The  area  of  the  openings  is  117  sq.  ft. 

The  paper  costs  38  ^  a  roll. 

The  border  costs  66|  ^  a  yard. 

Cost  of  putting  on  :  2  men  1|  days  each  at  $  2  a  day. 

Full  deductions  made  for  openings. 

Find  the  entire  cost  and  make  the  bill. 

3.  A  sitting  room  is  20  ft.  by  17  ft.,  and  10  ft.  high.     It 
has  3  doors  2  ft.  6  in.  by  7  ft.,  and  4  windows  31  ft.  by  e>  ft. 
How  many  rolls  of  paper  will  cover  the  walls  and  ceiling, 
deducting  J  the  area  of  the  openings  ? 

BOARD   MEASURE 

260.  A  Board  Foot  is  a  square  foot  of  the  surface  of  a 
board  1  inch  thick,  or  less. 


228 


PRIMARY   ARITHMETIC 


A  board  10  ft.  long,  1  ft.  wide,  and  1  in.  thick,  or  less, 
contains  10  board  feet  ;  but  a  beam  10  ft.  long,  1  ft.  wide, 
and  8  in.  thick  contains  8  times  10  board  feet,  or  80  board 
feet. 

The  number  of  board  feet  =  Length  (in  feet)  x  Width 
(in  feet)  x  Thickness  (in  inches). 

NOTE.  —  When  the  thickness  is  1  in.,  or  less,  the  number  of  board  feet 
is  the  product  of  the  length  and  width  in  feet. 

1.  How  many  board  feet  in  a  board  16  ft.  long,  12  in. 
wide,  and  1  in.  thick? 

2.  What  will  be  the  cost  of  10  planks,  each  12  ft.  long, 
10  in.  wide,  and  3  in.  thick,  at  $  12  a  thousand? 

3.  How  many  board  feet  in  a  board  14  ft.  long,  14  in. 
wide,  and  |  in.  thick  ? 

4.  How  many  board  feet  in  6  joists  16  ft.  long,  12  in. 
wide,  and  3  in.  thick  ? 


3  in.  wide 


VOLUME  MEASUREMENTS 

261.    The  Volume  or  Solidity  of  a  body  is  the  number  of 
cubic  units  that  it  contains. 

How  many  cubic  inches  in  a  block 
4  inches  long,  3  inches  wide,  and  2 
inches  thick? 

How  many  rows  of  cubic  inches 
are  there  in  the  bottom  layer  ?  How 
many  cubic  inches  in  each  row? 
How  many  cubic  inches  in  the  layer  ? 
How  do  you  find  it?  How  many 
layers?  How  many  cubic  inches  in 
the  2  layers  ?  How  do  you  find  it  ? 


VOLUME   MEASUREMENTS  229 

262.    The  answers  to  these  questions  give  us  the  following 


Rule  for  Finding  the  Volume  of  a  Solid 

Multiply  together  the  length,  breadth,  and  thickness, 
all  expressed  in  the  same  denomination. 

The  result  will  be  the  volume  expressed  in  cubic 
units  corresponding  to  the  unit  of  the  dimensions. 


1.  How  many  cubic  inches  in  a  block  12  inches  long,  6 
inches  wide,  and  4  inches  thick  ? 

2.  What  is  the  volume  of  a  block  of  marble  6  ft.  long, 

5  ft.  wide,  and  4  ft.  thick  ? 

3.  What  is  the  volume  of  6  bricks,  each  being  8  in.  by 
4  in.  by  2  in.  ? 

4.  The  solid  contents  of  a  block  are  720  cubic  feet.     It 
is  10  ft.  high  and  9  ft.  wide.     How  thick  is  it  ? 

NOTE.  —  To  find  one  dimension  when  the  solidity  and  the  other  two 
dimensions  are  known,  divide  the  solidity  by  the  product  of  the  two 
given  dimensions. 

5.  How  many  cubic  inches  of  space  in  a  box  10  in.  long, 

6  in.  wide,  and  4  in.  high  ? 

What  part  of  a  cubic  yard  is  the  space  in  this  box  ? 

6.  A  piece  of  marble  16  ft.  long,  12  ft.  wide,  and  9  ft. 
thick  can  be  sawed  into  how  many  blocks  of  a  cubic  foot 
each? 

7.  What  will  it  cost  to  make  an  embankment  containing 
54,270  cu.  ft.  of  earth  at  $.15  a  cubic  yard? 

8.  Find  the  number  of  cubic  inches  in  a  piece  of  ice  3  ft. 
long,  2|-  ft.  wide,  arid  18  inches  thick. 

9.  What  is  the  difference  between  6  cubic  inches  and  a 
6-inch  cube  ? 


230  PRIMARY   ARITHMETIC 

10.  If  300  cu.  ft.   of  breathing  space  is   required    for  a 
pupil,  how  many  pupils  should  be  seated  in  a  schoolroom 
30  ft.  square  and  10  ft.  high  ? 

11.  How  many  cubic  yards  of  earth  will  be  removed  in 
digging  a  cellar  36  ft.  square  and  6  ft.  deep  ? 

12.  How  many  books  9  in.   by  6  in.   by  1|   in.   can    be 
packed  into  a  chest  4  ft.  by  2  ft.  by  1|  ft.  ?     (Indicate  and 
cancel.) 

13.  How  many  cubic  "feet  of  snow  on  18  square  feet  of 
ground,  the  snow  being  9  inches  deep  ? 

14.  How  many  bricks,  8x4x2  inches,  will  it  take  to 
build    a   wall    16  x  8  x  1^    ft.,    no    allowance    for   mortar? 
(Cancel.) 

15.  How  many  cubic  inches  in  a  stick  of  timber  1  foot 
square  at  the  ends  and  8  ft.  long  ? 

16.  How  many  2-inch  cubes  may  be  made  from  a  piece  of 
wood  6  ft.  by  4  ft.  by  2  ft.  ? 

17.  How  many  loads   of   earth,  each   load   containing   a 
cubic  yard,  in  an  excavation  30  ft.  long,  26  ft.  wide,  and  14 
feet  deep? 

18.  A    cubic   yard  of   earth  makes   a   load.     How  many 
loads  must  be  excavated  for  a  cellar  32  ft.  long,  30  ft.  wide, 
and  61  ft.  deep  ? 

19.  A  brick  is  8  in.  long,  4  in.  wide,  and   2  in.   thick. 
How  many  will  it  take  to  build  a  wall  30  ft.  long,  20  ft. 
wide,  and  1 1  ft.  thick,  making  no  allowance  for  mortar  ? 

20.  The  volume  of  a  rectangular  solid  is  1200  cu.  ft.     It 
is  20  ft.  long  and  4  ft.  high.     How  wide  is  it  ? 

21.  How  high  is  a  room  that  is  24J  ft.  long,  20  ft.  wide, 
and  contains  4900  cubic  feet? 


WOOD  MEASURE  231 

WOOD   MEASURE 

263.  A  pile  of  wood  4  feet  wide,  4  feet  high,  and  1  foot  long 
is  a  Cord  Foot.     It  contains  how 

many  cubic  feet  ? 

A  pile  of  wood  4  feet  wide, 
4  feet  high,  and  8  feet  long 
contains  how  many  cord  feet  ? 
cubi  feet 

264.  The  answers  to  these  questions  give  us  the  following 


TABLE    OF    WOOD    MEASURE 

16  cubic  feet          make  1  cord  foot  (cd.  ft.). 

8  cord  feet    or  ) 

_,00       ,  .     r  >  make  1  cord  (cd.). 

128  cubic  feet       j 


How  many  cords  of  wood  in  the  following  ? 

1.  A  pile  18  ft.  long,  4  ft.  wide,  4  ft.  high. 

2.  A  pile  20  ft.  long,  8  ft.  wide,  8  ft.  high. 

3.  A  pile  50  ft.  long,  12  ft.  wide,  and  17  ft.  high. 

4.  What  is  the  cost  of  a  pile  of  wood  10  ft.  long,  8  ft. 
wide,  and  8  ft.  high  at  $4.50  a  cord? 

5.  How  high  must  a  pile  of  wood  be  made  to  contain  20 
cords,  if  the  pile  is  20  ft.  long  ? 

6.  How  many  cords  of  building  stone  in  a  pile  18  ft.  long, 
6  ft.  wide,  and  4  ft.  high? 

7.  How  many  cords  of  wood   can  be  piled  into  a  shed 
24  ft.  long,  18  ft.  wide,  and  12  ft.  high? 


232  PRIMARY   ARITHMETIC 

CAPACITY 

265.  Capacity  of  Cisterns. 

1.  A  wine  gallon  fills  231  cubic  inches  of  space.     How 
many  gallons  will  fill  a  cubic  foot  of  space? 

JJg2-8-  =  about  7  J  gallons.     Ans. 

NOTE.  —  It  is  sufficiently  accurate  in  estimating  large  liquid  capacities 
to  reckon  7|  gal.  to  the  cubic  foot. 

2.  A  cistern  is  5  ft.  square  and  6  ft.  deep.     How  many 
gallons  of  water  will  it  contain? 

Solve  both  ways  and  note  the  difference. 

3.  What   is   the   capacity   in    barrels    of    the    cistern    in 
Ex.  2? 

4.  How   many  barrels  of  water  in  a  cistern  7  ft.   long, 
4|  ft.  wide,  and  5|  ft.  deep  ?     (Indicate  and  cancel.) 

5.  What  is  the  capacity  in  barrels  of  a  tank  3  ft.  by  4^  ft. 
and  4|  ft.  deep? 

6.  How  many  gallons  of  water  in  a  tank  whose  capacity 
is  150  cubic  feet  ? 

7.  How  many  cubic  feet  in  a  cistern  that  will  hold  1500 
gallons  of  water? 

266.  Capacity  of  Bins. 

8.  A  bushel  fills  2150.42  cubic  inches  of  space,  which  is 
1^  cu.  ft.,  nearly. 

NOTE.  —  In  estimating  large  quantities  of  grain  it  is  sufficiently  accu- 
rate to  reckon  1J  cu.  ft.  to  the  bushel. 

9.  How  many  bushels  of  grain  will  a  bin  hold  that  is  6  ft. 
long,  5  ft.  wide,  and  4  ft.  deep?     (Indicate  and  cancel.) 

Solve  both  ways  and  note  the  difference. 

10.  How  many  bushels  in  a  bin  that  contains  150  cubic 
feet? 

11.  How    many    cubic    feet    in    a   bin    that   holds    150 
bushels? 


PERCENTAGE 


267.     To  THE  TEACHER.  —  Before  teaching  percentage  review  thor- 
oughly Questions  of  Relation  and  Division  of  Decimals. 

Questions  of  Relation  may  be  solved  by  means  of  hun- 
dredths. 


1.  How  much  is  -ffa  of  20  ?     Ans.  5. 

2.  5  is  fijfc  of  what  ?     Ans.  20. 

3.  5  is  how  many  hundredths  of  20  ?     Ans.  -f 

Another  name  for  hundredths  is  per  cent.  Thus,  -ffa  is  25 
per  cent,  yf^  is  8  per  cent,  .16  is  16  per  cent,  .05  is  5  per 
cent. 

Per  cent  means  by  the  hundred  or  on  the  hundred. 

The  sign  of  per  cent  is  Jo.  25  per  cent  is  25^,  6  per  cent 
is  6^>,  50  per  cent  is  50^. 

In  performing  operations  per  cent  is  used  generally  as 
decimal  hundredths. 

Using  the  sign  ft,  Examples  1,  2,  and  3  become  as  follows  : 

NOTE.  —  These  questions  may  be  solved  as  in  Art.  177. 

a.  How  much  is  25  </o  of  20  ? 

20  x  .25  =  5.     Therefore  25  %  of  20  =  5. 

b.  5  is  25  Jfe  of  what  number  ? 

Since  20  x  .25  =  5  5  -*•  .25  =  20.     Therefore  5  is 
of  20. 

233 


234  PRIMARY   ARITHMETIC 

c.    5  is  what  per  cent  of  20  ? 

Since   20  x  .25  =  5,  5  -*-  20  =  .25.      Therefore   5    is 
25^  of  20. 

What  principle  is  used  in  solving  questions  b  and  c  ? 

Question  a 
Find  the  result  and  form  questions  b  and  c  : 

4.  How  much  is  8^  of  50  ? 

5.  How  much  is  5/o  of  200  ? 

6.  How  much  is  12  ^  of  150  ? 

7.  lOjfc  of  60  sheep  are  how  many  sheep  ? 

8.  50^o  of  300  men  are  how  many  men  ? 

9.  2  ft  of  30  bushels  are  how  many  bushels  ? 

Question  b 
Find  the  result  and  form  questions  a  and  c 

10.  16  is  25/o  of  what  number  ? 

11.  15  is  10^)  of  what  number  ? 

12.  210  is  1^)  of  what  number? 

13.  20  sheep  are  5  ft  of  how  many  sheep  ? 

'  14.   40  pupils  are  10  ^  of  how  many  pupils  ? 

15.  80  horses  are  16^  of  how  many  horses  ? 

Question  c 

Find  the  result  and  form  questions  a  and  b. 

16.  20  is  what  %  of  80  ? 

17.  10  is  what  </o  of  200  ? 

18.  50  is  what  <fr  of  500  ? 

19.  25  boys  are  what  per  cent  of  100  boys  ? 

20.  15  pounds  are  what  per  cent  of  60  lb.? 

21.  What  per  cent  of  80  men  are  40  men  ? 

Find  the  result,  form  the  other  two  questions,  and  solve 
each. 


PERCENTAGE  235 

22.  5</o  of  40  apples  are  how  many  ? 

23.  $15  is  10/o  of  what? 

24.  12  yd.  is  what  <fo  of  48  yd.  ? 

25.  How  much  is  60  fo  of  200  bushels  ? 

26.  40  men  are  5^fc  of  how  many  men  ? 

268.  Percentage  is  a  process  of  solving  questions  of  rela- 
tion by  means  of  hundredths. 

269.  Read  the  following  Questions  of  Relation : 
Question  a.    How  much  is  5%  of  200  ?     Am.  10. 
Question  b.    10  is  5%  of  what?     Ans.  200. 
Question  c.    10  is  what  %  of  200  ?     .A^s.  5%. 

These  three  kinds  of  questions  form  the  basis  of  a  great 
variety  of  practical  computations,  which  are  classed  under 
the  general  head  of  Percentage. 

270.  Every  question  in  percentage  involves  three  elements: 
the  Rate  per  cent,  the  Base,  and  the  Percentage. 

271.  The  Rate  per  Cent  is  the  number  of  hundredths  taken. 
In  question  a,  what  is  the  rate  per  cent  ? 

272.  The  Base  is  the  number  of  which  the  hundredths  are 
taken.     In  question  a,  what  is  the  base  ? 

273.  The  Percentage  is  the  result  obtained  by  taking  a 
certain  per  cent  of  a  number.     In  question  a,  what  is  the 
percentage  ? 

How  much  is  8%  of  $200  ? 

SOLUTION.  —  8%  of  $200  =  200  x  .08  =  $  16.  We  now  have  the  three 
elements,  as  follows : 

8%  is  the  rate,  $200  is  the  base,  and  $16  is  the  percentage. 
Since  $200  x  .08  =  $16,  the  percentage; 
$16  -4-  .08  =  $200,  the  base ; 
and  $16  +  $200  =  .08,  the  rate. 


236  PRIMARY   ARITHMETIC 

274.  Therefore,  when  any  two  of  these  elements  are  given, 
the  other  may  be  found,  thus  : 

Base  x  Rate  =  Percentage  ; 
Percentage  -5-  Rate  =  Base  ; 
Percentage  -*-  Base  =  Rate. 

275.  Tell  which  elements  are  given,  and  which  one  is  re- 
quired, in  question  a  ;  in  question  b  ;  in  question  c. 


To  find  the  Percentage  when  the  Base  and  the  Rate 
are  given,  multiply  the  Base  by  the  Rate. 


1.  A  boy  had  $4.00,  and  spent  10%  of  it  for  a  book. 
How  much  did  the  book  cost  ? 

To  THE  TEACHER.  —  In  solving  any  problem  in  percentage,  the  pupil 
should  first  state  the  question.  The  question  in  Ex.  1  is  "  How  much 
is  10%  of  $4.00?  " 

2.  A  farmer  had  100  sheep  and  sold  20%  of  them.     How 
many  did  he  sell?     (Write  the  question,  then  solve.) 

3.  A  man  having  500  acres  of  land  gave  20%  to  his  son. 
How  many  acres  did  his  son  receive  ?     (Question.) 

4.  If  I  buy  goods  for  $400  and  sell  them  at  a  loss  of  5%, 
how  much  do  I  lose?     (Question.) 

5.  Write  a  problem  having  $500  for  the  base  and  4%  for 
the  rate. 


To  find  the  base  when  the  Percentage  and  the  Rate 
are  given,  divide  the  Percentage  by  the  Rate*. 


PERCENTAGE  237 

6.  $40  is  10%  of  what? 

Solve,  then  state  questions  a  and  c. 

7.  A  man  sold  goods  at  50%  profit,  and  thereby  gained 
1200.     What  was  the  cost  ? 

First  state  the  question.     ($200  is  50%  of  what?) 

8.  A  boy  paid  40  cents  for  a  book,  which  was  10%  of  his 
money.     How  much  money  had  he  ?     (Question.) 

9.  A  man  sold  20  sheep,  which  was  20%  of  his  flock. 
How  many  sheep  were  there  in  the  flock  ?     (Question.) 

10.  '10%    of  my  salary  is  $160.       What  is  my  salary  ? 
(Question.) 

11.  By  selling  cotton  at  5%  below  cost  I  lose  $200.    What 
was  the  cost  of  the  cotton?     (Question.) 

12.  A  grocer  gained  $50  by  selling  goods  at  10%  profit. 
What  did  the  goods  cost  ?     (Question.) 

13.  I  sold  a  bicycle  at  an  advance  on  the  cost  of  20%  and 
thereby   gained   $10.     What    did    I   pay   for  the  bicycle  ? 
(Question.) 

14.  A  man  pays  $300  rent,  which  is  20%  of  his  salary. 
What  is  his  salary  ?     (Question.) 


To  find  the  Rate  when  the  Percentage  and  the  Base 
are  given,  divide  the  Percentage  by  the  Base. 


15.  $50  is  what  per  cent  of  $500  ? 
Solve,  then  state  questions  a  and  b. 

16.  By  selling  a  bicycle  that  cost  $50,  a  dealer  made  a 
profit  of  $10.     What  was  his  gain  per  cent  ?     First  state  the 
question.      ($10  is  what  per  cent  of  $50  ?) 


E'"S 


238  PRIMARY   ARITHMETIC 

17.  In  a  school  of  900  pupils  450  are  girls.    What  per  cent 
of  the  pupils  are  girls  ?     (Question.) 

18.  A  boy  had  80  cents  and  spent  20  cents.     What  per 
cent  of  his  money  did  he  spend?     (Question.)     What  per 
cent  of  his  money  did  he  save  ?     (Question.) 

19.  From  a  farm  containing  400  acres  32  acres  were  sold. 
What  per  cent  of  the  farm  was  sold  ?     (Question.) 

20.  A  farmer  had  200  sheep  and  sold  50  sheep.     What  per 
cent  of  his  sheep  were  sold  ?     (Question.)     What  per  cent 
were  not  sold?     (Question.) 

21.  In  a  spelling  lesson  of  20  words  Lucy  misspelled  5. 
What  per  cent  did  she  misspell?      (Question.)     What  per 
cent  did  she  spell  correctly?     (Question.) 

SIMPLE  INTEREST 

276.  l.    I  borrow  $500  for  1  year,  and  at  the  end  of  the 
year  I  repay  the  money  and   6^  for   the  use  of  it.      How 
much  do  I  pay  for  the  use  of  $  500  ? 

2.  How  much  must  be  paid  for  the  use  of  $  50  for  1  year 
at  5  ft?  at  7fo? 

3.  How  much  at  5jfe  per  annum  must  I  pay  for  the  use 
of  $1000  for  1  year  ?  for  3  years  ? 

4.  I  loan  James  Barnes  $500  at  6jfc.     At  the  end  of  2 
years  he  pays  me  in  full.     How  much  does  he  pay  me  ? 

277.  Money  that  is  paid  for  the  use  of  money  is  called 
Interest.     The  money  for  the  use  of  which  interest  is  paid 
is  called  the  Principal,  and  the  sum  of  the  principal  and 
interest  is  called  the  Amount. 

Interest  at  6  ft  means  6  ^  of  the  principal  for  1  year. 
12  months  of  30  days  each  are  usually  regarded  as  a  year 
in  computing  interest. 


SIMPLE  INTEREST  239 

Oral.     5.    What  is  the  interest  of  $  100  for  3  years  at  6  ft  ? 

SOLUTION. —  $100  Principal. 

.06  Rate. 

$  6.00  Interest  for  1  year. 
3 


$  18.00  Interest  for  3  years. 

6.  What  is  the  interest  of  $ 80  at  5  ft  for  2|  years  ? 

7.  What  is  the  interest  of  $  1000  at  5  Jo  for  2  yr.  6  mo.  ? 

8.  What  is  the  interest  of  $100  at  6/0  for  1  year?     For 
1£  year  ?     For  2  yr.  6  mo.  ?     For  3  yr.  3  mo.  ? 

278.    When  the  time  does  not  include  days,  find  interest 
as  follows  : 


Rule  for  Finding  Interest 

Multiply  the  principal  by  the  rate  per  annum  and 
that  product  by  the  time  in  years. 


9.    What  is  the  interest  of  $  297.62  for  5  yr.  3  mo.  at  6  Jfe  ? 
SOLUTION.—  $  297.62 

r\n 

NOTE. —  Final  results  should  not  in- 


£17.8572^  clude  mins>      Mi}ls  are  disregarded 

IGSS  than  5,  and  called  another  cent  if  5 


892860  or 


$93.75.      Ans. 
Find  the  interest  of : 

10.  $384.62  at  6  %  for  2  yr. 

11.  1463.75  at  7/o  for  3  yr. 

12.  $250.50  at  8/0  for  Syr. 

13.  $685.20  at  4%  for  6  yr. 

14.  $596.15  at  5^  for  2  yr.  3  mo. 


240  PRIMARY   ARITHMETIC 

15.  $386.42  at  5<fo  for  6  yr.  5  mo. 

16.  $  950.16  at  10  <fo  for  4J  yr. 

17.  $283.25  at  6/0  for  2  yr.  8  mo. 

Find  the  amount  of  : 

18.  $284.10  for  3  yr.  2  mo.  at  7fc. 

19.  $364.24  for  1  yr.  1  mo.  at  6/0. 

20.  $282.50  for  5  yr.  9  mo.  at  5/o. 

21.  $298  for  4  yr.  3  mo.  at  6/0. 

22.  $  389  for  7  yr.  10  mo.  at  5  ft. 

279.    When  the  time  includes  clays,  we  find  interest  by  the 
following 


Rule  for  Finding  Exact  Interest 

To  compute  exact  interest,  find  the  exact  time  in 
days  and  consider  1  day's  interest  as  3-^  of  1  year's 
interest. 


1.  Find  the  exact  interest  of  $358  for  74  days  at  7/o. 

SOLUTION. — $358  x  .07  =  $25.06,  1  year's  interest.     74  days' interest 
is  3^  of  1  year's  interest.     ^  of  $25.06  =  $5.08.     Ans. 

Find  the  exact  interest  of : 

2.  $324  for  15  d.  at  9%. 

3.  $253  for  98  d.  at  4/o. 

4.  $624  for  117  d.  at  1%. 

5.  $153.26  for  256  d.  at  5%. 

6.  $620  from  Aug.  15  to  Nov.  12  at  670. 

7.  $540.25  from  June  12  to  Sept.  14  at  8fo. 

8.  $7560  for  90  days  at  5fo. 

9.  Find  the  exact  interest  at  5  ft  on  a  note  dated  Jan.  14, 
1896,  and  paid  March  31,  1896,  for  $  832. 


TOPICAL   REVIEW 


280.  l.    Write  in  words  5007. 

2.  Write  in  figures  fourteen  thousand  seventeen. 

3.  Write  in  figures  CCXI. 

4.  Write  in  Roman  245. 

5        Arid-          COQOt-OiCOrHQOOit-OCD 

o.     2i.uu.        CM  rt<  T-H          o  t~  CM  co  co  »-O  o 

CO  CM  GO    Ci    t— 

6.  From  twenty-four  thousand  eight  hundred  eight  take 
twelve  thousand  nine  hundred  nine. 

7.  If  you  have  24  cents  and  spend  8  cents  for  a  tablet 
and  5  cents  for  a  pencil,  how  many  cents  have  you  left? 
Indicate  the  operation  by  signs. 

8.  Divide  35,702  by  53. 

9.  Write  two  prime  numbers. 

10.    What  is  the  quotient  of  24  x  56  divided  by  7  x  12  ? 
Indicate  and  cancel. 

COMMON   FRACTIONS 

281.  1.    Write  an  improper  fraction  whose  value  is  more 
than  1.     Write  an  improper  fraction  whose  value  is  1. 

2.  Change  |  to  a  fraction  whose  denominator  is  40. 

3.  Change  to  lowest  terms  ^j-. 

4.  How  many  eighths  in  fifteen  ? 

5.  Write  two  like  fractions. 

6.  Change  to  common  denominator  and  add :  9,  f ,  |,  ^. 

241 


242  PRIMARY  ARITHMETIC 

7.  $  141  +  $  9  3  _  1 16 1  =  what  ?     Write  a  problem  using 
these  numbers. 

8.  The  sum  of  two  fractions  is  ^.     One  of  them  is  f . 
What  is  the  other  ? 

9.  15f-5i  =  ?     3|x5J  =  ?     28i-2f=? 
10.    Add:  28f,  171,  15|,  81. 

282.  l.    Write  a  proper  fraction,  an  improper  fraction,  a 
mixed  number,  and  an  integer,  and  use  them  in  one  problem. 

2.  Write  a  complex  fraction. 

3.  What  is  a  factor  of  a  number  ?     What  is  the  greatest 
common  divisor  of  two  or  more  numbers  ? 

4.  If  ^  of  my  money  is  invested  in  land,  |  in  houses,  and 
the  remainder  is  deposited  in  the  bank,  what  fraction  of  my 
money  is  in  the  bank  ? 

QJ3 

5.  Find  the  value  of  9    *  ,  +  1  of  i  -s- «. 

I  ot  I 

6.  Reduce  to  lowest  terms  ||-|. 

7.  The  sum  of  two  fractions  is  If.      One  of  them  is  f . 
What  is  the  other  ? 

8.  A  man  owned  |  of  a  ship  and  sold  ^  of  his  share. 
What  part  of  the  ship  did  he  sell  ? 

9.  A  man  had  $500  in  the  bank.     He  drew  out  -I  of  it. 

o 

How  much  did  he  draw  ?     (Question.) 

10.    A  man  sold  50  sheep,  which  was  ^  of  his  entire  flock. 
How  many  sheep  in  the  flock  ?     (Question.) 

DECIMAL   FRACTIONS 

283.  1.   In  the  number  32.6,  what  would  be  the  value  of 
the  2  if  it  were  removed  one  place  to  the  right  ?     What 
would  be  its  value  if  removed  one  place  to  the  left  ? 


TOPICAL   REVIEW  243 

2.  Which  is  the  greater,  50  thousandths  or  5  hundredths? 

3.  Take  one  thousandth  from  one  thousand. 

4.  Multiply  2£  by  2.84. 

5.  Multiply  100  by  .01. 

6.  1.111  -  .01  =  ?      1  -f-  .1  =  ?      .1  -  1  =  ? 

7.  Change  to  decimals  :  |,  |-,  J,  |. 

8.  Write  .0000054  as  a  common  fraction. 

9.  Write  as  a  decimal  fraction,  thirty-four,  and  three 
thousand  four  hundred  six  ten-millionths. 

10.    Write  as  a  decimal,  15  5-10000. 

284.  1.    Make  out  a  receipted  bill  of  the  following  :  66  Ib. 
pork  at  121  ^;   143  ib.  veal  at  16|  ^  ;  48  boxes  strawberries  at 
16|^;   60  doz.  eggs  at  16|^. 

Mr.  A  is  the  buyer,  and  Mr.  B  the  seller.     In  multiply- 
ing use  the  aliquot  parts  of  $1. 

2.  How  do  you  locate  the  decimal  point  in  any  product  ? 
In  any  sum  ? 

3.  Change  62|  and  83 J  each  to  a  common  fraction. 

4.  Divide  28.78884  by  1.25  and  have  four  decimal  figures 
in  the  quotient. 

5.  Divide  .001  by  1000. 

6.  What  cost  1650  oysters  at  50  cents  a  hundred  ? 

7.  What  is  the  cost  of  3783  ft.  of  pine  lumber  at  $16  a 
thousand  ? 

8.  What  is  the  cost  of  7384  tons  of  coal  at  $5  a  ton? 

285.  l.    What  is  the  cost  of  80  tablets   at   16f  ^  each? 
(Use  the  aliquot  part.) 

2.    At   33^  a   yard,  how  many  yards  of   linen  can  be 
bought  for  $9?     (Use  the  aliquot  part.) 


244  PRIMARY   ARITHMETIC 

3.  In  the  number  66.6,  what  is  the  value  of  the  first  6? 
The  second  6  ?     The  third  6  ? 

4.  Which  is  the  greater,  f  or  |,  and  how  much  ? 

5.  John   spent   .75   of   his   money.     What   part   of   his 
money  had  he  left? 

6.  Find  the  cost  of  these  articles  purchased  by  J.  D.  Fox 
from  John  Grouse  Jan.  10,  1882,  and  make  out  the  bill  in 
proper  form  : 

4  Ib.  coffee  at  25^  a  pound. 
18  Ib.  sugar  at  6^  ^  a  pound. 
4  gal.  of  molasses  at  50^  a  gallon. 
16  Ib.  of  rice  at  8^  ^  a  pound. 

7.  How  many  bushels  of  wheat  at  $  .90  a  bushel  must  be 
given  for  9  pieces  of  cloth,  each  containing  40  yards  at  $  .50 
a  yard  ?     (Cancellation.) 

8.  The  lesser  of  two  numbers  is  4603.85  and  their  differ- 
ence is  835.007.     What  is  the  greater  number  ? 

9.  John   gave    away    30    of    his   marbles.       How   many 
remained  if   he  had  200  marbles  at  first? 

10.    200  is  T2^  of  what  ? 

DENOMINATE    NUMBERS 

286.     1.    How  many  bushels  of  apples  at  50^  a  bushel  must 
be  given  for  15  Ib.  of  tea  at  40  j^  a  Ib.  ?     (Cancellation.) 

2.  From         7  mi.         40  rd.         9  yd. 
take  4  mi.         17  rd.          8  yd. 

3.  How  long  is  a  fence  that  extends  around  a  field  124 
rd.  long  and  78^  rd.  wide  ?     (Draw  diagram  of  field  and 
label  each  side.) 

4.  Define  Compound  Number  and  write  one. 


TOPICAL   REVIEW  245 

5.  If   a   peck   measure    is   one-quarter   full,  how   many 
quarts  does  it  contain  ? 

6.  How  many  bushels  in   1152  pints  ? 

7.  Three  quarts  of  milk  are  taken  from  a  two-gallon 
pail.  How  many  quarts  remain  ? 

8.  How  many  tons  in  6000  pounds  ? 

9.  What  will  4^  Ib.  of  indigo  cost  at  $  .05  an  ounce  ? 

10.    What  will  it  cost  to  build  15  yd.  of  fence  <it  58^  a 
foot? 

287.  1.    How  much  ro.pe  is  there  in  3  balls,  if  there  are 
20  yd.  1  ft.  in  one,  18  yd.  1  ft.  8  in.  in  another,  and  9  yd. 

2  ft.  11  in.  in  the  third  ? 

2.  At  $  2.40  a  dozen,  what  will  8  handkerchiefs  cost  ? 

3.  John  had  $25  and  spent  $15  for  a  suit  of  clothes. 
What  part  of  his  money  did  he  spend?     (Question.) 

4.  The  floor  of  a  room  12  ft.  wide  is  covered  by  24  yd. 
of  carpet.     How  long  is  the  room  ? 

5.  At  $  |  a  yard,  how  many  yards  of  cloth  can  be  bought 
for  $25?     (Solve  by  cancellation.) 

6.  Reduce  25  sq.  yd.  6  sq.  ft.  to  square  inches. 

7.  From  1J  sq.  miles  of  land  I  sold  a  farm  160  rd.  long 
by  100  rd.  wide.     How  many  acres  are  left  ? 

8.  Reduce  36,940  pints  to  higher  denominations. 

9.  How  many  feet  in  a  mile  ? 

288.  1.    How  many  acres  in  640  sq.  rods  ? 

2.  Show   the    difference    between   a   3-foot    square   and 

3  square  feet. 

3.  A  rectangle   contains   320  sq.  yards  and  is  20  yards 
long.     How  wide  is  it  ?     (Make  a  drawing  of  the  rectangle 
and  label  the  sides.) 


246  PRIMARY  ARITHMETIC 

4.  At  $18  a  ton,  what  is  the  cost  of  3000  Ib.  of  hay? 

5.  At  $  -|  a  pound,  what  will  2  pounds  of  tea  cost  ? 

6.  What  cost  3  Ib.  8  oz.  of  butter  at  30  ^  a  pound  ? 

7.  I  bought  8  cwt.  10  Ib.  of  sugar  for  $  81  and  sold  it  at 
12  ^  a  pound.     What  was  the  gain  ? 

8.  Find  the  area  of  a  floor  16J  ft.  long  and  4  yd.  wide. 

9.  How  many  gallons  of  water  will   a   cistern   contain 
that  is  7  ft.  long,  4^  ft.  wide,  and  4|  ft.  deep  ? 

10.    How  many  bushels  of  grain  will  a  bin  hold  that  is 

6  ft.  x  5  ft.  x  4  ft.  ? 

289.     l.    How  high  is  a  room  that  is  24J  ft.  long,  20  ft. 
wide,  and  contains  4410  cubic  ft.  ? 

2.  A  square  mile  of  land  may  be   cut  into   how  many 
80-acre  farms?     (Show  by  a  diagram  as  well  as  by  figures.) 

3.  Change  ^  of  a  ton  to  pounds. 

4.  3  oz.  is  what  part  of  a  pound  ? 

5.  Reduce  to  higher  denominations  369,426  cu.  inches. 

6.  How  many  cords  of  wood  can  be  piled  into  a  shed 
16  ft.  by  10  ft.  by  8  ft.  ?     (Indicate  and  cancel.) 

7.  How  many  cords  in  a  pile  of  wood  86  ft.  3  in.  long, 

7  ft.  6  in.  high,  and  4  ft.  wide  ? 

8.  How  many  bushels  will  a  bin  contain  that   is  9  ft. 
long,  4  ft.  wide,  and  6  ft.  deep? 

9.  Find  the  cost  of  9^  tons  of  coal,  if  ^  of  a  ton  cost 
$3.00. 

10.    How  many  rods  of  fence  are  required  to  enclose  a  lot 
20  rods  wide  and  3  times  as  long  ? 


ANSWERS  TO  HEATH'S  PRIMARY  ARITHMETIC 


Article  31. —4.    438.      5.    395.      6.    495.      7.    413.      8.   575.      9.    455. 

10.  347.       11.    3196.       12.    3846.        13.    3549.        14.    $2480.45.       15.    469. 
16.    4139.      17.    5354.      18.   $549.88.      19.    $732.98.      20.   6115.     21.   8915. 

22.  18,441.      23.    21,365.      24.    .$771.40.      25.    $1287.873.      26.    $821.191. 

27.  $577.189.      28.    890,407.      29.    103,019.       30.    $10,290.28.       31.    1364. 
32.   $240.75.        34.    31,014.        35.    273,420.        36.    875,935.        37.    51,543. 
38.    $41,981.17.      39.    $136.09.     40.    373,915.     41.    176,880.      42.  651,021. 
43.   $511.233. 

Article  32.  —  1.    41  peaches.     2.   41  scholars.      3.   98  sheep.     4.    87  bu. 

5.  $1.30.     6.    101  trees.     7.    80  qt.     8.    133  mi.     9.    126  fowls.     10.    $2.20. 

11.  62  years.     12.    71  houses.     13.    52  minutes.  .14.  43  fish.     15.  2057  miles. 

16.  $54.05.     17.    521  bu.     18.   658  pages. 

Article  43.  — 1.  2145.    2.  6927.    3.  3698.    4.  5499.    5.  1474. 

6.  27,997.   7.  18,338.   8.  17,082.   9.  81,482.   10.  68,004.   11.  4134. 

12.  71,359.      13.    8422.      14.    11,036.      15.    5347.      16.   8983.      17.    $1.032. 
18.    $8.233.         19.    $24.025.        20.    $19.687.         21.   $10.         22.    $12.082. 

23.  $1.052.     24.    $50.68.     25.    7529.     26.    25,350.     27.    21,996.     28.   3252. 
29.    6039.     30.  4127.     31.    $2341.64.     32.   $80.308.     33. '7726.     34.   11,369. 
35.    $23.967.      36.    41,276.       37.    $813.875.       38.  $2.33.       39.    166  acres. 
40.    $149.36.       41.    27  gal.       42.   73  oranges.      43.   163  acres.       44.   36yd. 
45.    49  sparrows.       46.    $  125.        47.   63  cents.       48.  95  eggs.       49.   27  qt. 

Article  44. —1.  237  bu.  2.  39  mi.  3.  $174.  4.  $1.99.  5.  $4.35. 
6.  252  mi.  7.  $268.  8.  $.43.  9.  83  papers.  10.  $99.  11.  447  pupils. 
12.  $151.  13.  15  years.  14.  $8.01.  15.  61.  16.  132  sheep.  17.  410  bu. 
18.  162.  19.  59  acres. 

Article  61. —  1.   7776.      2.   11,544.      3.   17,415.      4.   14,728.      5.   56,196. 

6.  54,600.      7.   33,432.      8.   96,728.      9.   15,996.      10.   34,314.      11.    70,784. 
12.   21,528.     13.    14,553.     14.    79,001.      15.   8288.      16.   27,006.     17.    11,124. 
18.   $788.20.       19.   $944.46.       20.   $912.87.       21.   $973.648.       22.   $431.31. 
23.  $1661.175.    24.  $11,042.21.    25.  $857.088.     26.  $902.060.     27.  $7285.185. 

28.  $1046.464.  29.   $10,098.72.  30.   $9967.12.  31.   $73,671.50. 
32.    $16,252.81.       33.   $63,677.16. 

Article  62.  — 1.  62,000.  2.  516  sheep.  3.  392  pounds.  4.  $504. 
5.  $3.60.  6.  2880  rods.  7.  8800yd.  8.  $17.50.  9.  583  mi.  10.  384  trees. 
11.  $15.  12.  $19.35.  13.  784  pounds.  14.  $8.10.  15.  $63.  16.  $105. 

17.  36,960ft.      18.   20,000  pounds.      19.   $2304.      20.   $10.32.      21.    $1926. 
22.   5030.      23.   870  acres.      24.   $49.50.      25.    1728  pens.      26.   2616. 

Article  73.  — 1.   28.     2.   62^.     3.    113^,     4.   28rV     5.   52|3.     6.    5(y7. 

7.  31 J}.     8.   1219.    9.    59^,     10.   99r\.     11.    ll}-\.     12.    123ff.     13.   80T%. 
14.    153.22.         157302.         16.    32f4.        17.    71  ^        18.   40^.         19.   200*«. 
20.    223f£.        21.   34i|?-.        22.   80}f.       23.   47 H.        24.    79A-        25.    300^. 
26.    lOOlJ.       27.   00p.       28.    17f|.       29.    1664J.        30.   215J?.        31.    18fj. 
32.    74U.       33.    63015.       34.    10l'«-f.       35.   99f|.       36.   241  A.       37.   595JJ. 
38.    283 jj.       39.    673$ j-       40.    687|f. 

247 


248  PRIMARY  ARITHMETIC 

Article  83.  —  1.   360  mi.         2.    178  bu.         3.    45  cents.         4.    153  tons. 

5.  54  rd.     6.   82  da.      7.    109.      8.    84  ploughs.     9.    202  acres.     10.    $4.625. 

11.  415  pk.          12.    52  wk.          13.    $3287.          14.    $4.20.          15.    1760yd. 

16.  125  overcoats.       17.    38  hours.       18.    72.       19.    36  gal.       20.    120  tons. 
21.    106  acres.      22.    24  stoves.      23.   33J  da.      24.    49  wk. 

Article  85. —1.   56.         2.    14.        3.    70  cents.        4.    16  hr.        5.   24  hr. 

6.  $20.83.        7.    $76.80.        8.    $22.14.        9.    $42.        10.    14|f.        11.  90  da. 

12.  $244.       13.   656  mi.       14.    $3924.        15.    340  miles.       16.    4fi  pounds. 

17.  $768.     18.  $965.     19.  38  times.     20.  55  months.     21.  12.     22.   5  years. 
23.  $159.33.      24.    33  tons.      25.    16  tablets.      26.    Carriage  182,  horse  183. 
27.  $72.             28.    Edward  $4.03,  Henry  $2.93,  John  $5.19.            29.    $13. 
30.  $65.28.       31.    $50.       32.    960  sheets.       33.    259  sheep.       34.    40  farms. 
35.  $192.40.         36.   $1590.  '      37.    24  acres.         38.    $3.69.         39.   $11.50. 
40.  48T%  pounds.            41.    46  miles  an  hour.            42.    264.            43.    $469. 
44.  $284.25.       45.    $41.       46.    70  hours. 

Article  97.  —  1.  2-5-3.  2.  2.2-2.3.5.  3.  2  -  3  -  7.  4.  3-2.11. 
5.  2-5-11.  6.  5-3-7.  7.  2.11-3.7.  8.  5.3.3.  9.  3.3.3.7. 

10.  5.7-19.  11.  3-13.11.  12.  5-5.17.  13.  2-3-3-23. 

14.  3.7.7.23.  15.  23-29. 

Article  100. —1.  4788.  2.  2.  3.  18.  4.  5J.  5.  3f.  6.  1J.  7.  63J. 
8.  12  bushels.  9.  20  yards.  10.  21 /v  11.  1  111  bushels.  12.  25  sacks. 

Article  106.  —  1.  12.  2.  21.  3.  15.  4.  56.  5.  12.  6.  20.  7.  16. 
8.  12.  9.  8.  10.  2.  11.  15.  12.  9.  13.  11.  14.  63.  15.  9. 

Article  111.— 1.    270.       2.   36.        3.   48.       4.   240.      5.     720.       6.   72. 

7.  420.     8.    560.     9.    7560.     10.    1400.     11.    630.     12.    192. 

Article  115. —  1.    10.      2     14.      3.    17.     4.    20.     5.    10.      6.    6.      7.    35. 

8.  20.      9.    10.       10.    3.       11.    29.      12.    3.       13.    218.      14.    93.      15.    300. 
16.    18.     17.    9.     18.   40.     19.    5.     20.    36  +  15  +  16  +  38.     21.    16  -  4 ;  y. 

5+  17;  (5  +  17)  -nil.    22.3  +  5+7.    23.2  +  5  +  6.    24.   $  10.16  -  $4.40. 

26.   60-(18+12).        27.    (18  +  5)-8.        28.    ($  1.00  +  $  .75  +  $2.50) -$2.75. 
29.   $5.18- ($1.50 +  $.75).  30.   4  +  (3  x  2).  31.    (4  +  3)  x  2. 


32.    4x3  +  2.       33.    4  x 
36.   18  x  18  -  144.       37. 
(5  x  150). 
Article  132.  —  1.   f. 
8.    A-       9.    tff       10.   i. 

(3  +  2).        34.    84-5x6.       35.    (72 
6  x  (11  -  6).        38.    (53  +  63)  x  4. 

2.    f.       3.    i        4.    TV       5.    if-       6. 
11.    H.       12.    fi        13.    1.       14.    i 

-  42)  x  4. 
39.    55^  + 

i       7.    J. 
15.    T^. 

16.    11.      17.   Mj 

f.       18-    &• 

19.   Ty      20.    I 

21.   4. 

22.    i. 

23.    J 

24.    i       25 

.    f 

26.    11. 

27 

.   i.      28.    11. 

29. 

|.     30. 

i- 

31. 

i      32. 

'  f 

33.    ff 

Article 

137.- 

-17.    -V-. 

18.    ^ 

19.   1% 

i.         20 

.    is-1-. 

21.   -1 

22.    W-- 

23.    a; 

!-•      24. 

4T8"T 

.      25. 

26. 

Vo1-       27 

W-. 

28.    1$ 

"J1- 

29.   *f  Ji. 

30.    i 

-!<p.     31. 

~t 

P.      32. 

~w~- 

33. 

32_3.         34>      11049 

.     35.    A 

:!-- 

38.    ifp. 

37. 

fc#UL. 

38. 

2W_2. 

39. 

i§f£.        40.    -^ff^.       41.    -ff^-. 

42.    if  p. 

43.    i 

fifl.     44. 

4 

IF- 

Article 

142.- 

-1.   47}. 

2 

•    16&. 

3.   20f.     4.   30^. 

5. 

30A- 

,     6.   21 

3T' 

7.   60$.     8. 

21  4  -, 

,     9.    161f. 

10.    134 

Ii     11 

.    52 

iV     12- 

24!}}V 

13.    27 

ir 

14.    248JJ. 

15. 

26if 

16.    191. 

17. 

19iJ 

.        20. 

21.   91 

22.        2/4y^^; 

Ar+     14.' 

7           1 

15,  36, 

50 

2     30, 

36,  20 

3 

25,  36, 

20 

4 

14,  12, 

27> 

ANSWERS  249 

6,  9,  10,  5        g     30,  72,  100,  105        -     360,  25,  36,  32        g     6,  9,  10,  7 

12  120  40  12 

135,  108,  80,  162    1Q   25,  28,  30,  32    n    15,  12,  20,  14    12  48,  45,  30,  110 

180  40  30  120 

Article  154.—  1.  If  2.  1.  3.  1JJ.  4.  2J.  5.  2J.  6.  1TV 
7.  1H.  8-  1J.  9-  2/2V  10.  7iJJ.  11-  2AVV  12.  2}J.  13.  9JJ. 
14.  44.  15.  5f.  16.  6  AT.  17.  16T%.  18.  4J.  19.  7-&.  20.  6J. 
21.  28if.  22.  23f  23.  3f.  24.  66if.  25.  47||,  26.  126TV  mi. 
27.  208|bu.  28.  $240ff  29.  259^  yd.  30.  lOfi  yd.  31.  $25ff. 
32.  241}JJA. 

Article  158.  —1.  •&.  2.  i.  3.  |.  4.  5|.  5.  2|.  6.  12TV 
7.  4TV  8.  9f  9.  6f.  10.  4J.  11.  if.  12.  T\.  13.  7V 

14.  T%.        15-   Ml-        16.   iJ  •  a%.        17.   If        18.   10|£.        19.   4J. 
Article  162.  —  1.   61.        2.   3-*,         3.   2f        4.   3£.        5.   6}.        6.   6if. 

7.  5f.   8.  41.   9.  5-f.   10.  7f.   11.  1.   12.  41J.   13.  2f.   14.  11. 

15.  4§.   16.  15.   17.  llj\.   18.  3TV   26.  108.   27.  1139.   28.  1634J. 
29.  1064TV   30.  1616.   31.  26rV   32.  3171.   33.  498J.   34.  1828J. 
35.  234.    36.  7546. 

Article  165.  —  1.   ff.       2.   |.       3.   T\.       4.-  1.       5.   i.       6.   ¥\.       7.   \. 

8.  g.      9.    ^2T.      10.    ^\.       11.    if.       12.    15.       13^  322.       14.    17J.       15.   2^. 

16.  1}.        17.   9f.         18.   396.        19.   32.         20.   36.         21.   9f.        22.   205. 
23.   309.          24.    72.          25.   323.          26.   750.          27.    1818.          28.   f  .  21J. 
29.   }J  -  if       30.   $35fJ.       31.   $115^.       32.   .130Jf.        33.   Elder,  74|^  ; 
younger,  49|§.        34.    15Jf  days. 

Article  169.  —  1.   T3r.         2.   \.         3.   &.         4.   Tf7.        5.   if.  6.   T\. 

7.   if.        8.    H.        9.    TV.        10.   i        11.   f.        12.    J.        13.   ||.  14.   A- 

15.   i.       17.   6|J,       18.   76|f.       19.   359J.       20.   77J.       21.   3^.  22.   4-i|. 
23.   66^.        24.   1637|f.        25.   ft-^V        26. 


Article  173.—  4.   li.         5.   1TV          6.   if         7.   f.        8.   1J.        9.   3J. 

10.  llf.         11.    aVV        12.   J.        13.   AV        14.   21.         15.    llf         16.    12. 
17.   TV        18.   £.         19.   i.         20.   4J.         21.   3.         22.   2T«T.         23.   fH- 
25.   9^.       26.    TV       27.   2J.       28.   TV       30.   791.       31.   88}}.       32.    76if 
33.   28^4T.          34.    12,451|.          35.   8001T\.          36.    8279/7.          37.   3822Jf 
38.   574T2T  rods.        39.    10  days.         40.   $4f.        41.   $31.        42.   44  barrels. 

Article  176.  —4.   27.     5.   23J.     6.   3}-|.     7.   2VV     8.    It}.     9.   If.     10.  5. 

11.  32.     12.   Jft.     13.   4^4T.     14.   $1201.     I5-   14  rods-     16.    14  tons. 
Article  177.  —6.   9.         7.   10.         8.   16.         9.   9.         10.   12.        11.   25. 

12.  20.          13.   6.          14.   15.          15.   21.          16.   30.          17.   40.          18,   i. 
19.   f.        20.   f.        21.   f.        22.   f.        23.   f.        24.   49.        25.   f        26.   3<>. 
27.   i}.          28.   28.  29.   209.          30.   i.          31.   20.          32.   42  marbles. 
33.  56  marbles.      34.  f  .      35.  70  acres.      36.  1  left  ;  }  spent.      37.  280  sheep. 

Article  178.  —  14.   $81  1. 

Article  180.  —  12.  24  hats.  13.  20  pounds.  14.  24  doz.  15.  24  pounds. 
16.  30yd.  17.  18  knives.  18.  $3.  19.  112. 

Article  182.  —  1.  $  1851.  2.  $  34J.  3.  32  J.  4.  Difference  i  greater. 
5.  $90f.  6.  $200.  7.  380^  barrels.  8.  Diminish  ^  ;  ^  9.  2JJ.  10.  10T67. 
11.  $3i.  12.  $.65f.  13.  13fyd.  14.  f  ;  f.  15.  f  |  ;  ff.  16.  100  sheep  ; 
50  sheep.  17.  TV  18.  125  sheep.  19.  $.08}.  20.  $2.  21.  51}  Ib.  22.  $6}. 
23.  i.  24.  120'days.  25.  50  pupils.  26.  $1.50.  27.  $f  28.  8^. 

Article  188.  —  1.   .25.     2.   .85.    3.    .326.    4.  .6.     5.  .16.     6.  .384,     7.  .49. 


250  PRIMARY   ARITHMETIC 

8.  .5.  9.  .06.  10.  .015.  11.  .025.  12.  .11.  13.  .09.  14.  .500.  15.  .50. 
16.  .9.  17.  .1.  18.  5.40.  19.  8.2.  20.  64.683. 

Article  189.  -21.  jfo.  22.  ^.  23.  ^V  24.  12TV  25.  6ffo. 
26.  TVoV  27.  TJfo.  28.  TW  29.  ^.  30.  A.  31.  5ft-  32.  5T^. 
33.  5^.  34.  5T%o_  35.  5r§^. 

Article  190.—  36.  ^;  .4.  37.  ^  ;  .75.  38.  ^  ;  -125. 

39.  16rf&;  16.48.  40.  12&  ;  12.4.  41.  &  ;  .6.  42.  ^  .06. 

43.  To6<ro;  -006-  46.  .282.  47.  .56.  48.  .7.  49.  .600. 

Article  194.  —  1.   Three  hundred  sixty-eight  thousandths. 

2.  Eight  hundred  ninety-four  thousandths. 

3.  Five  thousand  three  hundred  twenty-eight  ten-thousandths. 

4.  Two  thousand  fifty-three  ten-thousandths. 

5.  Twenty-five  and  six  hundred  twenty-three  thousandths. 

6.  Seven  and  sixty-three  ten-thousandths. 

7.  Twenty-eight  and  three  thousand  five  ten-  thousandths. 

8.  Twenty-eight  thousand  nine  hundred  sixty-two  hundred-thousandths. 

9.  Fifteen  and  sixty  thousand   five  hundred  thirty-four  hundred-thou- 
sandths.     10.   Thirty-seven  and   five   hundred  thirty-seven   hundred-thou- 
sandths.    11.   Twenty-five  and  two-hundred  three  thousand  six  hundred  two 
millionths.     12.   Thirty-eight  and  six  millionths.     13.   Four  million  nine  hun- 
dred eighty-three  thousand  six  hundred  ninety  -five  ten-millionths.     14.   Four 
and  ninety-eight  thousand  three  hundred  sixty-nine  hundred-thousandths. 

15.  Forty-nine  and  eight  thousand  three  hundred  sixty-nine  ten-thousandths. 

16.  Four  hundred  ninety-eight  and  three  hundred  sixty-nine  thousandths. 

17.  Four  hundred  millionths.     18.   Four  ten-thousandths. 

Article  196.  —1.  .8.  2.  .29.  3.  16.284.  4.  .4584.  5.  .25. 
6.  .025.  7.  .0025.  8.  .00025.  9.  .000025.  10.  1650.464. 

11.  1001.00036.  12.  16.006.  13.  .000784.  14.  .00012.  15.  .0075. 

Article  200.—  1.  .5000;  .3650;  .4689.  2.  .18963;  .50000;  7.84000; 

.16005.  3.  .28000;  3.50000;  .00005;  .25600.  4.  .50000;  .05000; 

.00500;  .00050;  .00005.  5.  .046300;  .030000;  .100000;  .100010. 

6.  .380;  1.160;  .400;  78.592. 

Article  201.  -2.  J.  3.  &.  4.  }.  5.  if.  6.  Jf-  ?•  «• 
8.  i.  9.  f  10.  f.  11.  ^  12.  ?V  13 


15.    16}.         16.    dr         I?-    i&V         18-    &•         19-    *Vfr-         20.    }. 

Article  202.—  21.  |.  22.  f.  23.  TV  24.  T2^.  25.  &. 

26.  i£§.  27.  |.  28.  f  .  29.  £?$.  30.  16J  ;  2J  ;  34}. 

Article  209.  —  1.  .8.  2.  .75.  3.  .44f.  4.  .875.  5.  .15.  6.  .4. 
7.  .6.  8.  ,55J.  9.  .464.  10.  1J.  11.  .30.  12.  .5625.  13.  .125. 
14.  2.24.  15.  3.0625.  16.  .375.  17.  .0375.  18.  .32.  19.  .75. 
20.  2.09375. 

Article  210.  —  2.  25.4162.  3.  6.788.  4.  20.2603.  5.  194.425. 
6.  161.1095.  7.  25401.3123.  8.  64.4266.  9.  120.9384.  10.  38062.881. 

11.  25.2477.      12.    2018.7147. 

Article  211.  —  1.    19.8.        2.    1.535.        3.   2.85.       4.   2.455.        5.   6.85. 

6.  .996.        7.    10.9.        8.   2.206.        9.    254.844.        10.    14.185.        11.    3.727. 

12.  1.11.      13.    499.95.      14.    10.3844.      15.    13.775.      16.    .099.      17.    Same. 
18.    999.999.     19.   499.95. 

Article  212.  —  1.   .027.    2.   .2001.     3.   .15.     4.  .28.     5.  .008.     6.  28.8075. 

7.  286.3.      8.    17.29.      9.    1.      10.    .05028.      11.    26.586.      12.    7.1.      13.   41. 
14.   1111. 

Article  215.  —  10.    5.1.     11.   4.06  +  .      12.    331.      13.    10.1.      14.    111.1. 


ANSWERS  251 

15.  11110.  16.  17.5.  17.  70.  18.  626.66}.  19.  6266. 66 J.  20.  62.664. 
21.  62.66J.  22.  375.  23.  155.5.  24.  10.  25.  .1.  26.  .01.  27.  549.77. 
28.  11.94. 

Article  217.— 7.  .875;  .71f  ;  .8;  16,75;  25.875.  8.  A;  M;  t;  15i- 
9.  $60.  10.  20bbl.  13.  25  pk.  14.  $90.657. 

Article  223.  —  1.  .$88.90.  2.  $410.18^.  3.  $6.39.  4.  $143. 

5.  102.15.  7.  $417.175. 

Article  232.  — 1.  10,368;  13,825.  2.  5  ;  6J.  3.  216;  864.  4.  }  ;  4. 
5.  J;  J.  6.  $250. 

Article 237.  —  Written:    1.  400  oz.    2.   15,000 Ib.    3.  258 bullets.   4.  80^. 

5.  85ioz.     6.   5  oz.     7.  30  bags.     8.   44  oz.     9.  $3.72.     10.  292  oz.    ,11.  ^. 
Article  241. — Written:!.  5J  hours.     2.  744  hours.     3.  Winter.     4.  Yes. 
Article  242.  — 12.    5|.         13.    $1-1.         14.    $215.20.         15.    $9.00. 
Article  245.— 4.    645  in.      5.    773ft.     6.    204,978  in.     7.   81,701  sq.  yd. 

8.    25,679,196  sq.  in.           9.    790,596  cu.  in.           10.    127  pt.  11.    507  pt. 

12.  528  qt.       13.    146,794  gr:      14.   73,774  oz.      15.    $24.  16.    225,932  in. 
17.    35,640ft.       18.    19, 138,464  sq.  in.     19.    762,051  cu.  in.  20.    69,056  oz. 
21.    21,972  gr.         22.    1947  gi.         23.    24,000  sheets.         24.  39,180  min. 

Article  247.  —4.    3  mi.  4  fur.  20  rd.  5  yd.  2  ft.  8  in.  5.    6  mi.  20  rd. 

6.  17  A.  67  sq.  rd.  3  sq.  yd.  7  sq.  ft.  72  sq.  in.  7.  16  cu.  yd.  9  cu.  ft.  3  cu.  in. 
8.  2  tons  316  Ib.     9.  3  Ib.  7  oz.  18  pwt.  4  gr.     10.  60  gal.  3  qt.  3  gi. 
11.  5  bales.   12.  3  wk.  6  da.  5  hr.  13.  560  bu.  1  qt.  14.  5  Ib.  7  oz.  16  pwt. 

15.  7  Ib.  3  oz.  4  dr.  1  sc.  12  gr.  16.  17  tons  1682  Ib.  17.  43  G.  gro.  10  gro. 

7  doz.  4.   18.  21  bu.  2  pk.  4  qt.   19.  3  sq.  rd.  18  sq.  yd.  6  sq.  ft.  27  sq.  in. 
20.  2  mi.  192  rd.  2  yd.  21.  60  rd.  4  yd. 

Article  248. —1.   63.      2.    244  gi.      8.  34 \  gal.      4.    $2.60.  5.    4000  oz. 

6.  35,000  Ib.        7.    1032  bullets.       8.    30,320  dr.       9.    254  pt.  10.    423  qt. 
11.    $41.12.        12.    127  bu.  4qt.        13.    $19.50.        14.    $1.26.        15.    4  gal. 

16.  72  qt.     17.   $4.20.     18.    255  qt.     19.    24  qt.     20.    9  bu. 

Article  249.  —4.   21  bu.  3  pk.  7  qt.       5.    15  bbl.  25  gal.  3  qt.       6.   5  yd. 

2  ft.  9  in.        7.    13  bbl.  15  gal.  2  qt.  1  pt.       8.    10  bu.  1  pk.  2  qt.        9.    14  Ib. 

3  oz.  15  dr.     10.    3  bbl.  28  gal.  1  pt. 

Article  250.  —  2.  5  A.  104  sq.  rd.  2  sq.  ft.  3.  54  da.  21  hr.  29  min.  48  sec. 

4.  3  hr.  42  min.  40  sec.  5.  14  T.  19  cwt.  49  Ib.  14  oz.  6.  11  Ib.  4  oz.  1  dr. 

7.  4yd.  1ft.  2  in.     8.   10  da.  22  hr.  18  min.     9.  9  gal.  1  pt.  3  gi.     10.    2  dollars 
1  dime  4  cents  2  mills.  11.    2  Ib.  2  oz.  12  dr.  12.    2  gal.  3  qt.  1  pt. 

13.  11  ft.  10  in. 

Article  251.  —3.  155  yr.  6  mo.  23  da.         4.  3  yr.  11  mo.  25  da. 

5.  67  yr.  9  mo.  22  da.    7.  138  d.   8.  60  da.   9.  213  da.   10.  23  da. 

11.  127  da.     12.  37  da.    13.  102  da.    14.  120  da.    15.  332  da. 
Article  252.  — 2.  64  gal.  1  qt.  2  gi.  3.  101  bu.  1  pk.  4  qt. 

4.  6  T.  13  cwt.  25  Ib.   5.  33  oz.  11  pwt.  6  gr.   6.  178  gal.  1  pt.  7.  10  Ib. 

8.  352  bu.  3  pk;.  4  qt.   9.  58  hr.  40  min.  48  sec. 

Article  253.  —2.  10  bu.  3  pk.  7  qt.  3.  2  bu.  2  pk.  2  qt.  4.  3  qt.  1  pt.  3}  gi. 

5.  1  bu.  1  pk.  1  qt.  \\  pt.   6.  15  packages.   7.  12  T.  16  cwt.  90  Ib.  15  oz. 

8  35  packages.  9.  28  gal.  1  qt.  1  pt.   10.  21  gal.  \\  pt.   11.  31  gal.  2  qt. 

12.  1  T.  640  Ib.  13.  106  oz.  12  pwt.  14.  2  wk.  4  da.  13  hr.  122  min. 
Article  256.  —1.  22  sq.  ft.  ;  3168  sq.  in.    2.  606  sq.  ft.    3.  $66.00. 

4.  15  ft.  -  5.  105  sq.  ft.   6.  80  sq.  ft.  ;  11,520.    7.  32  rd.    8.  00  ft. 

9.  100  A. 

Article  257.  —  2.    64|sq.  rd.     3.    $  16.16f .     4.    $40.83J.     5.    311Jsq.  yd. 
8.    $37.80. 


252 


PRIMARY   ARITHMETIC 


Article  258.  —  3.  80  yd.  ;  84  yd.  4.  S46.66f.  5.  $48.22}}.  6.  40yd. 
8.  $6475.00.  9.  825  sq.  yd.  10.  $58.33}.  11.  2000.  12.  100  rd. 

Article  259.  —  1.  96  sq.  yd.  ;  4  sq.  yd.  ;  24  rolls ;  81|  sq.  yd.  ;  20A  rolls  ; 
$6.804;  $11.00.  2.  $  35.79$.  3.  28&  rolls. 

Article  260.  —  1.    16  bd.  ft.     2.    $3.60.     3.    16}  bd.  ft.     4.   288  bd.  ft. 

Article  262.  —  1.  288  cu.  in.  2.  120  cu.  ft.  3.  384  cu.  in.  4.  8  ft.  thick. 
5.  240  cu.  in.  6.  1728  blocks.  7.  $301.50.  8.  19,440.  9.  210  cu.  in. 
10.  30  pupils.  11.  288  cu.  yd.  12.  256  books.  13.  13}  cu.  ft. 

14.   4320  bricks.       15.    13,824  cu.  in.       16.    10,368  cubes.       17.    404|  loads. 
18.    231}  loads.       19.  24,300  bricks.       20.    15  ft.  wide.       21.    10  ft.  high. 

Article  264.  —  1.    2}  cd.  2.    10  cd.  3.    79J-J  cd. 

5.    32  ft.     6.    3|  cd.     7.    40J  cd. 

Article  265.  — 1.    7}  gal.         2.    1125  gal.         3.    35^  bbl. 
5.    17^  bbl.       6.    1125  gal.       7.    200  cu.  ft. 

Article  266.— 9.    96  bu.       10.    120  bu.       11.    187}  cu.  ft. 

Article  267.— 4.  4.  5.  10.  6.  18.  7.  6  sheep.  8.  150  men.  9.  6  bu. 
10.  64.  11.  150.  12.  2100.  13.  400  sheep.  14.  400  pupils.  15.  500  horses. 
16.  25%.  17.  5%.  18.  10%.  19.  25%.  20.  25%.  21.  50%.  22.  2  apples. 
23.  $150.  24.  25%.  25.  120  bu.  26.  800  men.  27.  50%. 

Article  275.  — 1.40^.      2.   20  sheep.       3.   100  A.       4.   $20. 
7.   $400.       8.   $4.       9.   100  sheep.       10.   $1600.       11.   $4000. 
13.   $50.      14.    $1500.      15.    10%.       16.   20%.       18.   25%;  75%. 
20.   25%.       21.   25%;  75%. 

•    $125.       8.   $6;  $9;  $15;  $19}. 

11.   $97.386.     12.   $100.20.     13.   $164.448. 
16.   $42.757.       17.   $79.31.       18.    $347.075. 
21.   $373.9! 
3.   $2.716. 


4.    $2250. 
4.    41}bbl. 


6.  $400. 
12.  $500. 
19.  80%. 


Article  277.  — 6.   $10.      7. 

Article  278.  — 10.   $46.146. 
14.    $67.066.        15.    $123.976. 
19.   $387.915.      20.   $363.698. 

Article  279.  — 2.   $1.198. 
6.   $9.07.       7.   $13.498.       8.   $93.205.      9. 

Article  280.  —  1.  Five  thousand  seven. 


2. 


17.   879.31. 
22.   $541.35. 
4.   $14.001. 
.775. 
14017.     3.  211. 


5.   $5.388. 
4.  CCXLX. 


10.  16. 

3.  TV   4.  120.    6.  11}.    7.  7|.   8.  f. 


5.  7.   6.  }Jf   7.  T»A-   8.  J-   9.  $300. 


3.    999.999.      4.    7.10. 


5.   .000001. 


5.  11899.    8.  673ff, 
Article  281. —2. 

9.  10}};  21  A-  ;  9|i.  "10.  701." 
Article  282. —4. 

10.  70  sheep. 

Article  283.  — 1.    2  tenths  ;  2  tens.      2.   Same. 

5.  1.     6.   111.1;  10;  .1.      7.    .6;  .25;  .331;  .625.      8.    ^1 
9.    34.0003406.         10.    15.0005. 

Article  284.  — 1.    828.72.          3.    f  ;  f .          4.    23.0310. 

6.  8.25.         7.    $60.525.         8.   $36920. 

Article  285. —  1.    $13.333.      2.    27yd.       3.    600  ;  60  ;  6  units. 
TL  greater.        5.   }.        6.   $5.61.         7.   200  bu.          8.    5438.857. 
marbles.         10.   800. 

Article  286.  — 1.    12  bu.       2.   3  mi.  23  rd.  1  yd.       3.    405  rd.      5.   2  qt. 
6.    18  bu.         7.    5  qt.         8.   3  tons.         9.    $3.60.         10.    $26.10. 

Article  287.  — 1.   48  yd.  2  ft.  7  in.          2.   $1.60.          3.  f<         4.    18ft. 
5.   40yd.     6.    33264  sq.  in.     7.   860  A.     8.    73  hhd.  18  gal.  2  qt.     9.    5280ft. 

Article  288.  — 3.    16yd.       4.    $27.       5.    $}.       6.    $1.05.       7.    $16.20. 

8.  198  sq.ft.         9.    1122T%  using  7J  ;  1119I3T  using  231.         10.    96.427+  bu. 
Article  289. —1.   9ft.      2.    8  farms.      3.    500  Ib.      4.    TV      5.    7  cu.  yd. 

24  cu.  ft.  1362  cu.  in.  6.    10  cd.  7.    20^  cd.  8.    173.569+  bu. 

9.  $38.        10.    160  rd. 


4. 
9.   1 


0 


. 
UNIVERSITY   OF  CALIFORNIA  LIBRARY 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


C  17  1917 


OCT  1? 


30m-l,'15 


VB   17247 


'OA/os 
K/37 

i 


